I see a lot of discussion here regarding the influence of listening to music but I am also curious about the influence of rhythmic training. This year I added rhythmic training as a warm up to all of my piano students lessons. I've been using an old staple 'Stick Control' (link below) to train the most basic LH/RH coordination and beat perception and have been amazed at the improvement across the board including myself since I work on this with them. I would compare the improved LH/RH coordination with improved conceptualization of a beat to a rising tide that lifts the ships of the beginner, the prodigy, the professional and the senior citizen student.
Stick Control is basically fine motor coordination and a bit of limb independence exercises, even if you are not a drummer, practicing stick control will improve your "handling" in any instrument. Or even in unexpected things, for example, while driving, I find heel-toeing very easy and natural (brake with right foot toe, press the clutch with left foot, change gear with right hand while steering with the left hand, rev-match with the right foot heel, let go of the clutch) probably because I've played the drums for almost 22 years now.
In the same note, as a fellow drummer, I can say that drummers that study melodic instruments tend to play their instruments serving the music way better. Piano is probably my second preferred instrument, I've always wanted to learn it, if you can guide to some starting material or equipment, I'd be happy to hear!
The only thing I'll add to this is the benefit of working with a metronome. With 88 keys and 10 fingers there is a lot pianists can get distracted by but when you strip it down to RH/LH eighth notes starting at 30 bpm you can really focus on generating a time feel!
A guide you say?! Funny you mention it this is what I've cobbled together for my students over the years. It's about time for me to give it another pass to further refine it but it is a reliable path towards basic keyboard proficiency. Let me know what you think.
https://www.amazon.com/Stick-Control-George-Lawrence-Stone/d...