Kentucky Gov. John Y. Brown is peddling his proposed gubernatorial succession amendment to the state constitution as vigorously as he once pushed encyclopedias and Colonel Sanders' Kentucky Fried Chicken. Under the present constitution, Brown, whose term expires in 1983, can only serve one term; the succession amendment would enable him and other state officials to succeed themselves.

Five of Brown's political and governmental colleagues, including two cabinet officers, have underwritten a $150,000 bank loan to finance a television advertising and direct mail blitz on behalf of the amendment between now and election day, Nov. 3.

The question is why Brown, who the Great Political Mentioner includes as a possible Democratic presidential candidate in 1984, is pushing the amendment. The obvious assumption is that he wants to to be reelected to give himself a base for a presidential run. Recently, however, he dropped a strong hint that he wouldn't run for governor again, saying that he would be "a most unlikely candidate for reelection" if it passes.

Jimmy Carter and Ronald Reagan demonstrated that an elective base not only isn't necessary for a successful presidential campaign, but also it might be a liability in terms of time and distraction; Brown wasn't in office when he ran for governor. Some political sources also believe that Brown is too lazy to take on a grueling presidential race and that most of the presidential ambition resides in his aides--and with his wife, former beauty queen and television commentator Phyllis George.