I've had a couple horses with partial sight problems in one eye, and they did act like yours does. They'd want to hold their head to the side when circling, and they'd suddenly spook when something appeared on that side.
If his right eye is the problem, then you could try temporarily blocking his vision on that side until you're on. This can be done with a blindfold or a helper or in any number of ways. Even just turning his head toward you as you mount, so that he sees you completely with his left eye and can't see you with his right eye, might help.
You block his view of your actions on that side, you do what you need to do, and you get him used to it. Then you try it without the blindfold, because even if he sees you he's used to the feel of you there, and is less likely to spook at it.
You may find the problem is not his vision, but is the weight, but once you know that you can address it. Put your weight in the stirrup without moving the rest of your body. He'll likely move away, but stay with him, keep trying, don't react aggressively but just keep doing it until he accepts it. Only then move on to swinging your leg over.
In general, a horse with impaired vision in one eye needs to be handled carefully until he's adjusted to the eye and is used to being handled. When moving around the horse, talk to him and keep a hand on him so he knows where you are.