On its third try, the Senate Commerce Committee yesterday finally cleared the tracks for President Carter's "Independent" nominee for the Amtrak board of directors.

Frank H. Neel, the Thomasville, Ga., air conditioning contractor and veteran of the 1976 "Peanut Brigade," was cleared by a 9-to-5 floor vote.

Although Carter had designated the former member of the Georgia State Democratic Committee as an "independent" member of the Amtrak board, the committee split on strict party lines, with all the Democrats favoring Neel and all the voting Republicans opposed.

Republican complaints that Carter was trying to circumvent the statute that says no party may have more than five members on the nine-person board had sidetracked the Neel nomination twice previously.

But yesterday, with Neel's chief critic, Sen. Robert P. Griffin (R-Mich.), occupied with floor duty on the Panama Canal treaties debate, Chairman Howard W. Cannon (D-Nev.) brought the nomination up for a third time. He had the proxies in his pocket to win.

Griffin still had one card to play, however, and late yesterday he played it. He put a "hold" on the nomination, meaning that it cannot be approved routinely by unanimous consent, and must be subject to debate and a roll-call floor vote.

With the Senate occupied with Panama for the foreseeable future, no one was sure when Neel might pass this final roadblock.

Griffin said last night that "there can be little question that loading a bipartisan board with closet Carter sympathizers circumvents that clear intent of the law. It looks like the cynical old politics has been born again -- only this time with a Georgia accent."

But Neel, in a letter to Cannon, provided a personal political history to support his claim to be an "independent," even though he campaigned in seven states for Carter in 1976.

He wrote that he had voted for the winning candidate in the last eight presidential contests -- Democrats Harry S. Truman, John F. Kennedy, Lyndon B. Johnson and Carter, and Republicans Dwight D. Eisenhower and Richard M. Nixon. He said he gave $75 to Nixon's campaigns and he and his wife have given $1,700 to Carter campaigns over the years.

Neel also came up with an endorsement of his credentials as a consumer representative from the National Association of Railroad Passengers, after assuring its representative that he favored increasing passenger service.

He has met almost every objection his critics have raised except one -- the fact he last rode a train in this country in 1964. Neel said last night, "I just don't have time to take a vacation and go by train."