I never actually used a clicker with my fourth horse because he picked up on a verbal “Good boy!” as the click before I could dig my clicker out. He was highly food motivated. He actually figured out that his actions affected the food before I even actively tried to use it! That’s why I used clicker/“Good boy!” training.
I did use R+ simultaneously with the usual pressure cue/release (is that N-?) of training under saddle. The pressure cue was removed, and the “Good boy!” followed by a carrot chunk in response to the correct action. My horse did slam the brakes on and look for his carrot. I was concerned about it being a problem later on, but he stopped looking for the food reward when he grew confident about the right response to my aids. He used to puff up a bit proudly and continue doing the thing when I said “Good boy!”
It was a cycle. New things got the anxious stop and turn for carrot, with the sense of “Was that really what you wanted? Did I get it right?” As confidence grew the stop got softer and then disappeared. I used voice and neck rubs/scritches as the reward more as he kept doing the thing.
I recently saw a video about an experiment on dogs. The dogs were trained to lie in the machine used for brain scans, and shown a toy which was immediately followed by either food or verbal praise. The dogs’ brains showed different responses to the reward types, with the verbal praise getting a much higher response.
Food is the usual reward, and probably the best way to get most animals’ attention. Non food rewards can be used as well, once the animal has developed the understanding of the action reward connection. Use of non food rewards allow for R+ training under saddle more easily.
The point of the click is to mark the instant of desired behaviour/response. It is the promise of reward coming, not instant reward. Clicking multiple times before rewarding does work to build a more complex response, which can become a single response/action. Like training to pick up a foot - first shift weight off the foot, then lift the foot, then allow the human to catch the lifted foot, then put it down, then hold the foot, then move the foot, then pick it out. It’s not necessary to wait until the lift is perfect before trying to catch the foot, and is better not to as that isn’t the end goal.
Last note: The first time I did clicker training was with my then 4yr old when he was healing from an injury. He was going well WTC under saddle at the time of the injury. When I started riding again I attempted to use clicker training under saddle, but he was entirely uninterested and irritated at being stopped to have a treat offered. While he has never been particularly food motivated, my experiences suggests that bringing the R+ into riding from the start might make it a better tool.