Use Vegetable oil or WD-40,
Soak the tape with a small rag. Then lay the soaked rag on the old tape and cover it with a piece of cellophane to keep it moist. This should pull the top off, repeat to get the glue residue off. When removing the glue residue a stiff toothbrush should remove it from the grain and pores.

Either of these won't pull your original finish, but you'll probably have some dis-coloration from the tape being on so long.
I've used this method on old antique dressers and document boxes multiple times with great results.

A Heat Gun can cause the Tape's adhesive to become tacky again... Depending on the grade of tape. Some were Low Tack- Others High Tack. If it Tacks up again it's possible you'll pull wood fiber. You don't need heat, you need to break down adhesion.

It'll work

Nearly 50 years of taping stuff !

Merry Christmas