I don't think "protective gear" is the answer to your problem, lol
. First of all, you would have no idea how your Amazon (or your other bird) would react to "the protective gear", it would probably scare the living hell out of him and he may not even want to get on your shoulder or be anywhere near you, both of your birds would probably freak out and take off if you tried to hold them wearing a big helmet and goggles! So let's abandon that idea.
I see a few glaring issues that are very likely causing the problems you guys are having with your Amazon. First off, a lot of birds will act/react very differently to you or while with you/on you if you're holding another bird at the same time. How do your Amazon and your Cockatoo get along and interact with each other? If it were me and I was wanting to start to make a real, concerted effort at getting close to my bird that wasn't friendly or close to anyone, I'd start out by committing a block of time EVERY SINGLE DAY to just spending time with that bird. I would completely stop trying to get your Amazon to come sit on you while you've got your Cockatoo on your other shoulder. It's not only causing your Amazon to be nervous, it's probably a serious source of jealousy for him, as it seems your Cockatoo is friendly, tame, and by default is probably interacted with a lot. Is this the case? You have to remember that both of your birds have the intelligence and the emotions of a 4-5 year old human toddler! So your Amazon likely thinks "Why would he think I want to sit on his shoulder when that other bird he is always playing with is on him already? Why is that the only time he ever shows any interest in me, when he's already got that other bird that he likes better with him?" If that sounds harsh then I'm glad, because that's the general feeling your bird very likely has.
How many hours per day do you spend with your birds, either with the Cockatoo (if he's the only one that you do spend time with) or with both? I would commit, at the very least, to spending 1-2 hours to start off (ideally it's 3-4 hours per day at a bare minimum, but you need to be with the Amazon separately at first) with your Amazon. If you want him to sit on your shoulder then do not have your Cockatoo on you. As already stated shoulder time is a privilege that comes with trust, so you need to correct his behavior, not wear "protective gear". However, just to see what happens, I would try allowing your Amazon to sit on your shoulder (no protective gear please) while your Cockatoo is not with you, either in a different room or put the Cockatoo in his cage. I'm willing to bet (if you haven't tried this already of course) that if you commit to spending one-on-one time with your Amazon, he will act very differently when your Cockatoo isn't with you. Just give it a try. If he does sit on your shoulder without biting or attempting to bite you need to vocally tell him what a good bird he is over and over (as you need to with everything he does that is good or loving, a lot of positive reinforcement!!!!) and give him a treat! Always positive reinforcement, never negative reinforcement or punishment! If he still does bite or attempt to bite at you then this is your starting point. No cockatoo around, if you put him on your shoulder and he attempts to bite you you firmly say "No bites" and immediately put him back on his cage top. This is where you start from. So every day, no cockatoo, you need to directly interact with just your Amazon. If he's sitting on his cage top then you need to sit next to him, as close as you can get, and talk to him. Reading to him works well, find a toy, puzzle, game, etc. that he likes, whatever you can find to entertain him and allow him to spend at least 1-2 hours directly interacting with you only. You should also do the same with your Cockatoo daily as well. Eventually you'll earn your Amazon's trust, it could happen tomorrow or it could take months, either way you need to commit to spending time with him every single day without the Cockatoo, and do just the same with the cockatoo. Eventually, once you earn your Amazon's trust and the two of you are bonding closely (same with the cockatoo) you should be able to have them both out in the same room with you if you're watching TV or whatever. You may never be able to have them both on you or directly interacting with you at the same time, in fact you probably won't, and this is why you need to make enough separate, quality time each and every day for both of them.
This is a really good example of why you should never get a second bird to entertain your current bird. I don't know your history as far as how long you've had each bird or anything, I'm not directing this at you, but rather using the situation you're currently in with your two birds to illustrate what the end result can be if you have a bird and you're thinking of bringing home a second bird to be a friend for your current bird. The situation the OP is in is exactly what can happen when you do this, and we get so many people posting the question of "Should I get another bird FOR MY CURRENT BIRD?". This is why our answer is always a resounding no. You'll end up needing to schedule a block of time to be with each bird separately if the birds don't get along or are jealous when they are both with you. I don't think the OP in this case had that happen, I think the situation, from what I can tell, is that the Amazon in your home has never been interacted with much or socialized much because he has never been very friendly or trustworthy. However, the Cockatoo is friendly, so you and your wife/girlfriend have always spent most of your time directly interacting with the cockatoo, and as you said (unfortunately), "your wife has your Amazon on her hand once a day". Now, while I understand the problem, you and your partner need to realize that this is unacceptable as a proper amount of interaction time daily with your Amazon, and if it continues he will never, ever trust either of you or become friendly. He needs to be socialized daily, he needs just as much time directly interacting with you guys daily as you spend with your Cockatoo, and they both should have a bare minimum of 3-4 out of cage hours per day, interacting with you guys directly. Your wife getting him off his cage top one time a day (probably not for long) doesn't cut it at all. 3-4 hours per day is always thought of as the absolute bare minimum time for interacting with a bird in your home, ideally it's longer than that. And if you're spending little to no time with your Amazon that is hurting him, but him knowing and seeing you not only ignoring him but also spending lots of time with your Cockatoo is a double whammy. So you both need to either commit to equal time interacting with both birds daily (at least a few hours with each bird separately), or your Amazon will never become socialized or friendly, plus, it's not fair to him. And keep in mind that "interacting directly" with your Amazon doesn't necessarily mean touching him. That will come in time. Rather, it means focusing what you are doing only on him, reading to him, playing with him, talking to him, etc.
"Dance like nobody's watching..."
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