This one goes even further back than the previous one, and in fact comes from what we historians term Ye Olde Days. The saying is: Under the Thumb.
(It’s another one I nicked from a recent TV programme.) One of the leading sports in Ye Olde Days was hawking, now known as falconry. The bird of prey has various ‘thingies’, as they known the sport (probably), attached to its legs which the owner uses to keep it under control when it’s perched on his arm. In order to allow him one hand and some of this other fingers free to do other things, he traps one of more ‘thingies’ between his thumb and his wrist or gauntlet – hence, he has got the bird Under the Thumb.