I would like to use assistive touch to wake up my watch screen like a wrist raise. This would make counting my patient’s pulses easier—I am a paramedic.

You can set your screen to stay active for 15 seconds OR 70 seconds. Perhaps the simpler solution would be to change the screen on time. Apple Watch App on iPhone > Display & Brightness > Wake Duration > Choose 70 seconds

If you tap the screen it usually stays on fir 14 seconds, where raise is only 4 seconds so yes, neither is suitable

You could add a Stopwatch or timer complication to your favourite face. Save 15 sec as favourite time.

and yes it will only ladt 14 seconds but you could get into the habit of flipping your wrist at 10 seconds.

Setting assistive touch will probably still have a 14 seconds display so pinching your fingers (or whatever) as opposed to twisting your wrist. So its Swings or Merry-go-rounds

https://m.youtube.com/watch?v=_j4-NTg3QsE

Use AssistiveTouch on your Apple Watch - Apple Support

"...Apple Watch App on iPhone > Display & Brightness > Wake Duration > Choose 70 seconds..."

Ah yes I forgot about that, but I avoided it because of battery life!

I don't use 70 seconds either, even though with the Ultra, the battery lasts forever. I just don't have a use need for the screen to stay active longer. But the OP does, so this would, I think, solve the issue for them.

I'm testing 70 seconds for myself to see how the battery goes. It seems it does go off if you drop the wrist and returns to 5 seconds when raised again which seems reasonable regarding battery life.

Since I know you charge your watch every night as I do, it shouldn't be a very negative hit on battery life.