It has not been unusual over the years for some bleary-eyed Maryland politician to be awakened by the phone ringing at midnight or 5 a.m. and find surgeon Ross Z. Pierpont, fresh from a hospital operating room, on the line for a political chat.

"I've gotten those phone calls, and I don't think there's a Republican who has run in an election with Ross who hasn't been called at, shall we say, an unusual hour," said Baltimore lawyer Joseph Ayd. "It's one of Ross' trademark."

Perhaps the same energy and nerve that allow Pierpont to make these late-night phone calls also account for his perserverance through five unsuccessful bids for political office and his current push for the Republican nomination for governor.

In this race, the Baltimore Sun and News-American polls recently showed him with 3 percent of the vote, while perhaps the best-known of his three opponents, J. Glenn Beall, was pulling 54 percent.

But the 61-year-old Pierpont, chief of surgery at Maryland General Hospital in Baltimore, is unmoved by these figures, which he said are "not properly reflective" of what is happening in the campaign.

Pierpont asserts that he is running "neck and neck" with Beall and has been for some time according to a secret "minipoll done for Beall by the Republican National Committee." An astonished Beall said he had "never heard of any such things."

And Ayd, who is running two Republican primary campaigns in other races, said of Pierpont's neck-and-neck assertion: "It is just that kind of boastfulness on his part that turns off a tremendous number of people who would otherwise res pect him."

But the baldish, bespectacled Pierpont, unbowed by such criticism, continues traveling the state at a furious pace talking to the public about his "Proposition 13 approach" to cut real estate taxes in Maryland.

Pierpont says he supports a referendum like California's Proposition 13 that would set the property tax rate at 1 percent of the fair market value of real estate, a change he promises would equalize real estate taxes across the state and in many areas, such as the city of Baltimore and Montgomery County, lower taxes for homeowners. He also supports a 2 percent ceiling on real estate tax increases per year.

Everybody else is talking about rearranging taxes, but I'm for reducing spending to actually reduce taxes," says Pierpont, who promised that he could chop $271 million from the $4.4 billion state budget through natural attrition and a freeze on hiring.

The second major theme Pierpont has concentrated on, in his campaign, is the revival of old campaign financing charges against front-runner J. Glenn Beall. Ignoring his two other rivals for the GOP nomination, Louise Gore and Carlton Beall (no relation to the other Beall), Pierpont talks instead of the approximately $250,000 in cash and check contributions J. Glenn Beall received in his 1970 campaign for the U.S. Senate from a secret White House fund known as the "townhouse operation."

Pierpont said Beall not only received the "tainted" money, but used it to supply "walk around" money to Democratic election day workers in Baltimore.

Beall said his only response is that "the funds were handled under the rules in existence at that time." The "townhouse" fund, which came to light during the Watergate hearings,was investigated by the Watergate special prosecutor's office, which found no wrongdoing by Beall or the other recipients.

Pierpont, who was born in Woodlawn, started working at the age of 8 after his father died, and worked his way through the University of Maryland and its medical school. He once recalled: "Every stitch I put on my back I bought myself."

But he now says his net worth is somewhere "over a million dollars" and he owns numerous stocks, real estate and oil wells and heads two private corporations of surgeons in Baltimore and Havre de Grace.

The self-made millionaire who is described by hospital colleagues as an "excellent surgeon" and by others as a "brillian businessman" believes that 1978 will be his year to win election.

Though he is spending only about $7,000 on this campaign, Pierpont said he has gotten "a million dollars worth of publicity in the past" during his races for governor, U.S. senator, mayor of Baltimore and Congress, and his name is well known.

The surgeon said he has never been discouraged by his previous political defeats because "If I've contributed to the stability or well-being of the state, even if I'm never elected, I will have done something valuable."

Pierpont said he believes it is important for citizens like himself, who are not professional politicians, to run for office. "I'd like to see more people of top caliber in business and other professions run for office," he said, adding that the problem with people who spend their whole lives in politics is that "they are always feeding at the public trough and become prostitutes."