First, welcome to the forum and congrats on the new-ish horse
. I would certainly love to see some pictures of him, I love Mustangs.
I always start my greenies in a simple loose ring snaffle, but that is just a personal preference. I would avoid a mechanical hackamore though, they aren't great on trained horses and can be a train wreck on a greenie that doesn't understand the basic concepts of pressure yet. A bosal can be a good tool, but it is very important to know how to properly use one. It is very easy to either skin up their nose/jaw or teach them to ignore it if handled improperly.
The most important thing, regardless of what you have on his head, will be repetition and reward. Whenever you are riding and ask for the stop, ask with both your seat and your hands, also, using a verbal "whoa" might help as well. Keep the pressure constant until he stops his feet and then immediately release pressure and take a neutral seat. Over and over and over again. At first, he will likely nose out and keep walking or tuck his nose and keep walking, sometimes they will walk sideways but just keep that constant light pressure until his feet stop (and most normal horses will eventually, I promise
). If he doesn't seem interested in stopping even with repetition, then start using one rein to stop him and work your way back up to two.
Teaching him the one-rein stop wouldn't be a bad plan of action either. Make sure that you have him supple and responsive to each side and take one rein until his feet stop. That is a tool that will come in incredibly handy if the day comes when he tries to buck or spook and bolt.
In my experience, the best way to get a horse over being mouth shy is to just treat them like any other horse and handle their mouth a lot. I use a bit on all of mine and I don't make a big deal out of bridling them, I just stay as soft and gentle as I can while I bridle them. I avoid letting the bit bump their teeth and I just move with them if they lift their head or back up or walk forward. If they are really bad about it, I will give them some kind of treat immediately after they accept the bit and lots of verbal praise/petting/scratching. Usually, after a few times when they figure out that being bridled really isn't
going to kill them, they relax about the whole issue and don't mind having their mouth handled so much.
But, his mouth shy issue will never get any better if you avoid it