I trained a horse that was almost blind in one eye, so, not totally the same. This horse would get very flustered when asked to turn in the direction of the bad eye..she would rear and buck a bit. So they brought her to me.
What I had to do was spend a lot of time(about 5 times my normal) on the ground with her to gain her confidence. When I was first working with her, she would not lunge, or even change direction on her bad side. So, I took it real slow, and used alot of voice commands, and constantly reassured her with my voice.
Then I just slowly progressed her into the saddle(she had been ridden prior, but with the above issues), I only rode her in the round pen for the first 5 or so rides, using voice commands and assurances when turning to her bad side. It took about 3 rides for her to start relaxing when I asked for her to move to her bad side. I think the voice commands and assurances helped her understand that I wasn't going to ask her to go toward "danger", and that she could trust me.
I then took her into the arena, she hadn't been in there before, so I had her walk in circles in the middle of the arena in both directions(so she could get a look at what it was all about from her good side going both ways). She was still a bit nervous for about the first 10 minutes, but gradually became better. I rode her for 6 more rides(maybe 5 or 7 - don't quite remember) in the arena, where I discovered when she did get nervous and buggery, I had to turn her so the her good eye was to the outside - which meant I had to turn her toward her bad side...this bothered her for the first few times. So, I worked on that constantly - had a tarp on the fence, put up a flag, etc. until she would one-rein stop without issue going to her bad side.
The first few rides out were not the greatest, but we took it slow and when she got nervous I just turned her in a tight circle and made her work and keep focus on me--while constantly assuring her with my voice.
I just progressed her from there. She will never be a solid trail horse, but her owner just wanted to ride around their place on her, so I took her there and rode her a few times to show her the sights...she is still going well, I think. They haven't asked me to come over and help her anymore.