She knows what is wanted she just doesn't want to do it. Tapping the air isn't a meaningless cue. At least not to me because safety is very important to me. It teaches the horse to get out of your space safely. Without making you get closer to the horse.
Oh, right. I got the idea from your post that you were just teaching this horse, not that she was already trained, knew what you wanted. If she truly knows what you're asking(so she used to do it reliably & now has stopped), then I'd strongly suspect she 'doesn't want to' due to a physical problem - something about backing up is causing her discomfort. Or perhaps she 'knew' this cue with someone else, and you're doing it a little differently, or not reinforcing/rewarding her for 'right' answers, so it's not working for her - she doesn't quite know it with you.
Assuming she isn't already well trained(& if she was
but is learning it doesn't work for her any more with you), the cue being meaningless was about *her*, not you(I imagine you wouldn't be doing it if it was meaningless to you!
). Many/most 'cues' we teach a horse are innately meaningless & we teach them by associating them with a behaviour they are reinforced/rewarded for. That is why I suggested teaching it up close first(& you say she 'doesn't want to' like that either), so you can be clearer, more direct, to get the response. If she doesn't understand, and you just get stronger(tapping the rope, her nose...) that will be equally as meaningless, and it is natural for a horse to get resistant/reactive about pressure they don't understand.
Think of it like communicating with a person who doesn't speak your language; they're not likely to learn better just because you shout louder or keep repeating yourself, but if you use an obvious gesture or guide them to do whatever, at the same time as you say the words, they will learn easily what they mean. IOW, if something's not working, change your approach, rather than just getting 'stronger' or repeating the same thing more.