The General Services Administration has been ordered to reinstate a second senior executive who was fired after a spending scandal revealed a culture of excess at the agency.

James Weller, a retired Army colonel who was in charge of federal buildings for GSA’s Southwest region, lost his job in 2012 amid revelations that a Las Vegas “training” conference was little more than an extravagant junket for 300 employees.

But a Merit Systems Protection Board judge ruled that GSA officials failed to prove that Weller, 60, was guilty of misconduct. While he attended the four-day Western Regions conference in 2010 and flew to Las Vegas for one of eight dry runs to plan it, he was not involved in the planning or aware that taxpayers paid $823,000 for the event, the judge ruled. He awarded Weller 19 months of back pay.

“Outside of his appearance at the final ‘dry run’ meeting, the appellant possessed no knowledge regarding the [planning meetings] until well after the fact, and thus was not in a position to contest or otherwise limit the travel costs associated with their frequency and composition,” Administrative Judge Ronald J. Weiss wrote in a 38-page decision released in March.

A year ago, the merit board awarded Paul Prouty, a career civil servant in charge of public buildings in GSA’s Rocky Mountain region, to be reinstated with back pay. Prouty did not attend the conference or any pre-planning meetings,though dozens of his employees flew to Las Vegas.

GSA has appealed both rulings.

“We are disappointed with the administrative judge’s initial ruling” in the Weller case, agency spokesman Dan Cruz said Thursday in a statement. While their back pay is on hold pending the outcome of the case, both executives were reinstated but immediately placed on administrative leave with pay, agency officials said.

Administrator Dan Tangherlini, appointed by President Obama to clean up the agency, has made significant changes and declared an end to what he described as a culture of excess.

Tangherlini has reorganized the buildings service and the department responsible for buying supplies for federal agencies, cutting down on redundancies and costs and stressing accountability.

He also led a government-wide effort to slash federal travel to conferences and unnecessary training seminars, and has focused on reducing the government’s real estate footprint to save money.

Weller and Prouty are two of 46 officials who were suspended, warned or reprimanded for their role in the Western Regions conference. Eleven were fired. GSA had recommended that organizer Jeffrey Neely, the Region 9 commissioner, be fired, but he was allowed to retire under civil service regulations.

About 250 other employees who attended the conference, revealed in 2012 in a report by Inspector General Brian Miller, were sent letters of admonishment, GSA officials said.

Lodging at an opulent hotel, entertainment by a $3,200 mind reader, after-hours parties in 2,400-square-foot loft suites, a $7,000 sushi reception, a bicycle-building exercise — all took place at taxpayers’ expense. The eight scouting trips cost $130,000.

Administrator Martha N. Johnson resigned under pressure and her top deputy, Public Building Service chief Robert Peck, was fired.

Miller referred criminal charges against Neely to the Justice Department, which so far has not brought any charges.

In an e-mail, Neely said, “I can only tell you I am enjoying retirement and my two new granddaughters.”