What worked for me is just practice the rhythm all the time when i was away from the horse. I would be driving down the highway saying “1-2-3-change, 2-2-3-change, 4-2-3-change” (for 4 tempis) or “1-2-change, 2-2-change, 4-2-change” (for 3s) over and over until I got the rhythm (with the cue for the change being on the word “change,” i.e., on change I would pretend to swing my leg back to cue the new lead. Depending on your horse (and you), you might add a tiny pretend squeeze of the new rein for the new flexion the beat before you say “change” so on beat 3 for 4 tempis, beat 2 for 3 tempis. When I was first getting it down I would almost swing my whole body to the new direction (in the car) just to get the feel for the swing. Remember, this is in the car or out walking the dog, not on the horse. Just keep singing the rhythm until you hear it in your sleep. The name of the game here is you need the rhythm down pat. It should sound like marching in your head. Get a metronome app and play it while you practice if you have to.
When you get to the point where you sing it in your dreams, try it on horseback. Only stick to one count at first (e.g., only do 3s, don’t go into the arena and do 3s and 4s the same day until you are good at one of them). Importantly, start singing the rhythm when you turn onto your line - don’t start singing it after you start the changes or you risk getting off the beat (at least that’s how it works for me). For instance, I turn onto the diagonal, immediately start singing the rhythm, then cue the change when I hit my first “change” in my head.
Hope this helps you as much as it helped me. Great to hear that the horse has it down - that makes things much easier!!