I just had to check what i actually do with my fretting thumb, and it turns out that i dont press at all. I just mrerely rest it on the back of the neck, so there's virtually no pressure at all
Funny thing, i've had the OP's problem in the back of my hand , which i assume is tendon, from the little finger to the wrist, and it sometimes becomes painful, and i've found that most times,
if i bend all fingers backwards with my other hand till i hear a faint crack, that this sorts it.
I guess the little finger is weaker than the others, and as I occasionally use the little finger ( and the 3rd ring finger too ) at times, i guess i'm creating a problem in that area