In the nearly 3,000 pages of interviews from the House impeachment inquiry released last week, President Trump often seems like a supporting character in someone else’s drama.

Aides struggle to please him. They fret about his fits of rage and do their best to anticipate his ever-shifting impulses and desires. Trump is an unseen and mercurial presence.

“President Trump changes his mind on what he wants on a daily basis,” said Gordon Sondland, the Trump megadonor-turned-diplomat who sought to help Ukraine’s new leader — desperate for American aid and an Oval Office meeting with Trump — understand what the president actually wanted from him.

Amid the torrent of testimony, it is easy to forget that the crux of the historic House impeachment inquiry boils down to a simple question: What did Trump want from the Ukrainians — and what exactly did he do?

To answer that question, Republicans and Democrats have cited the rough transcript of Trump’s July 25 call with Ukrainian president Volodymyr Zelensky — a conversation that witnesses have described as “improper,” “shocking” and a confusing mishmash of conspiracy theories, empty threats and non sequiturs.

Republicans have made the rough transcript and the chaotic nature of the Trump presidency a central part of their defense. “I read the transcript,” said Sen. Lindsey O. Graham (R-S.C.), a close ally of the president. “What I can tell you about the Trump policy towards the Ukraine is that it was incoherent . . . They seem to be incapable of forming a quid pro quo.”

Democrats are counting on using the testimony of those around Trump — a mix of aides, sycophants and serious-minded civil servants — to make clear exactly what Trump was demanding of the Ukrainian president on the July 25 call.

Senior U.S. officials working on Ukraine often seemed to live in a state of dread and confusion over what the president might do or tweet. Ambassador Marie Yovanovitch was clinging to her job in Kyiv this spring, amid a smear campaign organized by Rudolph W. Giuliani, the president’s personal attorney, when State Department officials told her to leave her possessions behind and come home on the first possible plane.

Her bosses in Washington didn’t fear for her safety; rather, they feared Trump. “They were worried that if I wasn’t physically out of Ukraine there would be some sort of public tweet from the White House,” she told lawmakers.

With Yovanovitch gone, the new team in charge of Trump’s Ukraine policy often struggled to make sense of his myriad grudges. In May a trio of officials that consisted of Sondland, Energy Secretary Rick Perry and special envoy Kurt Volker huddled with Trump in the Oval Office to share their favorable impressions of the Ukrainian president.

“They tried to take me down. They tried to take me down,” Sondland recalled Trump saying of the Ukrainians.

Most officials suspected Trump’s rage traced back to the conspiracy-theory conversations he was having with Giuliani regarding alleged — and unsubstantiated — Ukrainian interference in the 2016 election.

“I would love to see what Rudy was saying to him,” said a senior administration official involved in Ukraine policy, who spoke on the condition of anonymity to describe internal deliberations. “That’s the big unknown. That would put the puzzle pieces together.”

Giuliani often called Trump on his personal cellphone, so there was no record of when he called or what he talked about with the president, U.S. officials said.

Even the highest-ranking officials were flying blind. Whenever Giuliani popped up on the television in John Bolton’s West Wing office, the national security adviser would turn up the volume to try to learn what he might be telling Trump, said Fiona Hill, who oversaw Russia and Ukraine policy in the White House.

Meanwhile, Bolton issued orders to his aides to steer clear of Giuliani and his schemes.

Trump’s precise role in the Ukraine scandal is further muddied by unreliable witnesses, faulty memories and, in one case, a disembodied voice announcing a confounding order to freeze $391 million in desperately needed military aid to Ukraine.

On his July 25 call with Zelensky, Trump is clear regarding what he wants from Zelensky. “I would like you to do us a favor,” Trump said. He then pressed the Ukrainian president to investigate a widely debunked conspiracy theory, proffered by Russian President Vladimir Putin, among others, that Ukraine and not Russia had interfered in the 2016 U.S. election. Trump also asked Zelensky to investigate former vice president Joe Biden and his son Hunter, who had secured a lucrative position with a controversial Ukrainian gas company.

“It sounds horrible to me,” Trump said.

Less clear is whether Trump ordered a hold on the $391 million in military aid to shake down the Ukrainians. Senior U.S. officials first learned of the freeze during a July 18 video conference in which an off-camera staff person from the White House’s Office of Management and Budget said there was a hold on the aid, but would not say why.

“I and others sat in astonishment,” recalled acting ambassador William B. Taylor Jr., who had dialed in from Ukraine.

Trump has offered up different explanations for the hold, saying that he froze the aid because he was angry the Europeans weren’t doing more to help Ukraine. He also has insisted that he didn’t want to send the money to Kyiv because he was worried about corruption.

Top officials at the Pentagon and State Department spent much of July and August struggling to figure out why Trump had frozen the aid and how to get it flowing. The answers were vague and unsatisfying.

In August, Bolton asked the White House’s Ukraine expert to draft a presidential decision memo arguing for the resumption of the aid. Bolton’s plan was to present the memo to Trump during a meeting with Secretary of State Mike Pompeo and Defense Secretary Mark T. Esper, who also backed releasing the money.

The Cabinet officials gathered in the Oval Office, but it’s not clear what they talked about with the president.

“At least one report suggested the topic [of Ukrainian aid] never came up,” testified Lt. Col. Alex Vindman, who drafted the memo. Vindman received a second report that the aid was discussed but that Trump refused to make a decision.

Acting White House chief of staff Mick Mulvaney, who issued the order to stop the aid, last week defied a congressional subpoena for his testimony. Bolton’s lawyer has cryptically suggested that his client has important, new information to offer, but that he won’t testify until a court rules on the legitimacy of the congressional order.

That leaves Sondland as the witness who had the most frequent and direct conversations with Trump about Ukraine.

Sondland, though, has proved to be an unreliable narrator, subject to massive memory gaps, frequent misstatements and a tendency toward self-aggrandizement. He boasted to White House officials of frequent meetings with Trump but seems to have been exaggerating. “There were often times when he said he’d been in to see the president when other staff indicated to me that they did not believe he had,” Hill told lawmakers.

In his sworn testimony, Sondland struggled to recall his meetings with the president and other top U.S. officials, prompting flustered Democrats to wonder whether he was drunk or on some kind of medication that causes memory lapses. “You have a number of conversations with Ambassador Sondland. I just want to make sure in those conversations there was no indication he was under the influence of alcohol, correct?” Rep. Ted Lieu (D-Calif.) asked the acting ambassador to Ukraine.

Taylor replied that Sondland seemed sober.

In his testimony, Sondland comes off as a target of the president’s rages and a hapless seeker of his approval. “It was sort of a bad meeting,” he said of a May Oval Office briefing that he gave Trump on Ukraine.

He described his conversation with Trump just before the president’s July 25 call with Zelensky as “kind of a nothing call . . . He wasn’t really interested.”

In September, Sondland told top Ukrainian officials that their military aid wouldn’t flow until Zelensky announced on television that he would investigate the Ukrainian gas company that employed Biden’s son.

The Ukrainians pondered putting Zelensky on CNN. Sondland, eager to please Trump, suggested Tucker Carlson’s Fox News program.

Meanwhile, senior U.S. officials in Kyiv and Washington worried the entire scheme was illegal. “I think it’s crazy to withhold security assistance for help with a political campaign,” Taylor texted Sondland from Ukraine.

That text led to one last, quick phone conversation between Sondland and Trump that cuts to the core question of the impeachment proceedings: What did Trump want?

“I want nothing!” Trump yelled at Sondland. “I want Zelensky to do the right thing!”

The president then abruptly ended the call.

“I wouldn’t say he hung up on me,” Sondland said. “But it was almost like he hung up on me.”

This week House Democrats and Republicans will call their first witnesses for the public portion of the impeachment inquiry testimony. The Democrats will rely heavily on decorated military officers such as Vindman and longtime civil servants such as Yovanovitch and Taylor to make their case. The Republicans seem intent on putting the Bidens on trial.

Notably, Sondland, the witness from the closed-door round of questioning who spoke most directly with Trump about Ukraine, isn’t on either party’s witness list.

Aaron C. Davis contributed to this report.