My shaky hands during eyeliner work got so bad last winter I almost quit doing makeup. Started forcing myself into bed by 10 PM every single night, no excuses, and cut out all caffeine after 2 PM. After about two weeks, the jitters were just... gone. It’s crazy how much we ignore the basic stuff our bodies need.
That's a really good point about sleep, but I'd be careful saying it's always just fatigue. Sometimes shaky hands are a sign of something else, like low blood sugar or even a vitamin deficiency. I had something similar and my doctor had me check my B12 levels, which were way off. It's worth getting checked if the sleep fix doesn't hold.