Have you tried Finklestein's test? If you have overuse injury of the thumb tendon, you'll feel an intense jolt of pain with this maneuver. Rest, ice, brace until swelling subsides and gradual return to movement. I hope it's not this! (But if it is, you have a permanent excuse to never have to pluck chickens by hand!)
Don't know about thumb cramps but it works for leg cramps. Bite your lower lip...you'll know you are putting pressure on the right area of the lip if the cramp starts to subside. That's worked for me for years....must be some kind of acupressure point, as it really does work.
I get a lot of "almost cramps" and pain, fatigue in the fleshy part of my palm right behind the thumb when I have to do a lot of work with my hands, particularly with small items that require a lot of finger control, but I think it is related to arthritis.
I injured my left wrist holding a dog to keep him from going hunting lol the other I think is just this tiny keyboard on my phone I've been using to post in here
I'm surprised I don't get cramps in my hands with the amount of sewing I do. But my fingers do get stiff at times. When I get cramps it's in my feet and holy crap, it's bad