Hmm.. interesting. I've only ever heard of ball of thumb as the bit at the base, as you say "Thenar Eminence" is a name I've just been introduced to so thanks for that. Wikipedia suggests that nowadays it can also be used as the pad at the tip end, not at all confusing!
Anyway, on any instrument, if your fretting hand is on the neck in a club or cradling hold, so base of the thumb against the neck, try your maximum stretch 1st to 4th finger (we *are* all using your 4th finger, aren't we?). Now try it with the pad or tip of your thumb on the back of the neck.. gives me a good couple of inches more range, which especially on double bass means way better flexibility and far fewer position shifts.