James A. Rhodes would have a wonderful life were it not for the irksome provision of the Ohio constitution that once every eight years he has to let someone else be governor. By the end of this term in 1982, Rhodes will have been governor for 16 of the last 20 years, with Democrat John J. Gilligan filling the constitutionally mandated void.

Rhodes has been expected to challenge Sen. Howard M. Metzenbaum (D) in 1982, but sources in Columbus say he now is exploring a more appealing option: running for lieutenant governor, so he can keep a closer eye on "his" office. Rhodes recently discussed Senate life with former senator William B. Saxbe (R), who fled it in boredom to become U.S. attorney general, and agreed with Saxbe that sitting through endless committee sessions and marching dutifully to quorum calls would be a world-class drag for a free-spirited fellow such as himself.

If Rhodes drops out, Rep. John Ashbrook has a clear path to the Senate nomination but Ohio Republicans say there would be great pressure on either Rep. Clarence J. Brown or Cleveland's Seth Taft, rivals for the GOP gubernatorial nomination, to switch to the Senate race rather than let a conservative like Ashbrook be uncontested.