You reblogged an interesting Gaz post recently, do you have any more thoughts on him? It's been bugging me for a while that he says he regrets what he did to the bridgemen but hasn't actually... apologized or attempted to make amends or anything, but you seem optimistic? I haven't devoted much thought to him but it seems like you have at least a little
I have many thoughts, thanks for asking! (For those interested, this is the post that Zoli is referencing)
When it comes to making amends, it really depends on the size and insularity of the community you're living in, and the extent of the damage done. The purpose of making amends is to continue having a relationship with the person you hurt, or who hurt you. It's usually more important to make amends in already established relationships, in smaller, more insulated communities, and when the damage was less bad. People are encouraged to make amends with family members, members of their religious community, or neighbours, in part because the nature of the relationship will force you into proximity. Whether that amends is a full apology and acceptance of that apology, or a mutual agreement to pretend the other person isn't in the room, it serves to repair the relationship or at least establish a new normal so both parties can move forward without fear.
So why would Gaz want to maintain or repair his relationship with Bridge Four, when his only relationship with them previously was as a slavedriver? He would have to start a new relationship with them, and I don't think that's something anybody needs or wants. Given that they are all Radiants, there is enough proximity that they may see each other occasionally, but there's no need for them to interact, and Gaz understands that.
I think the way he's been acting, to be cowed when he sees them and generally avoidant of them, is actually the best way to show them that 1) he is no longer a threat to them; 2) he feels guilty for what he did. That's all Bridge Four really needs in order to move forward in the world without fear, and that's all they need.
Gaz can't undo the damage he did to Bridge Four, and everyone on Bridge Four hates his guts for good reason. Instead, he's moved on. He left his post where he had that power over people, and he's trying to become a better person who doesn't hurt people. In this case, I don't think an apology or any attempt at a future relationship with them is needed.
Ultimately, redemption looks like different things depending on context, and making amends isn't always necessary, and sometimes doesn't even make sense. Like for example I don't think it would be helpful for Dalinar to do a handshaking apology tour to the survivors of the Rift--it's clear that if he did that it's about him trying to rehabilitate his image rather than having any kind of positive effect on his victims, many of whom would likely rather not be in the same city as him, let alone the same room.
Gaz is letting himself be the villain in Bridge Four's story, because he knows he was. Sometimes the only gift you can give the people you've hurt is to leave them alone and never do that again to anyone else.