In the second inning tonight at Chase Field in Phoenix, 48-year old Julio Franco homered off of 43-year old Randy Johnson. That's 91 years in total on that homer.
I'm going with that as the oldest pitcher-hitter pair until I find out otherwise. So far other "old pairs" I've found include a 36-year old Eddie Joost homering off a 46-year old Satchel Paige in 1953 and a 39-year old Cy Williams homering off of a 43-year old Babe Adams in 1926. Those both add up to 82 years.
Each homer Franco hits adds to his record for "oldest player to hit a home run."