There is nothing you can do that will guarantee your brother starts talking to you. In fact. Trying to do this may actually be making it worse. Leave him alone for a while and let him stay as angry as he needs to be until he is ready to turn around. You’ve made your apology, followed up with it, and the only time things softened was when you left him alone. I’d follow this fact: things got better only when you paid less attention to him.
Forgiveness involves two parts: unforgiveness and forgiving the other person. People can carry the unforgiveness for a long time, but there isn’t much the unforgiven can do about it. It is inside your brother. You’ve made your amends — now he has to figure out how to deal with the unforgiveness of you. That is on him to figure out.
To put this into perspective person ‘A’ could be mad at person ‘B’ and person B might never be seen or talked to again. For all practical purposes, person B could have disappeared from the planet, but person A would be walking around with unforgiveness. It is a separate set of feelings and actions from forgiving person B. In fact, it has nothing to do with person B after a while because the unforgiveness resides inside person A.
Forgiving someone is an outward gesture, but softening to be able to do that is an inside one. This involves dealing with unforgiveness, and holding onto a grudge. This is for your brother to figure out how to do — or not.
Sometimes holding on to unforgiveness is a way to keep from taking responsibility for your actions. You can stay angry at someone else rather than take responsibility for you’re your part in a circumstance.
This doesn’t mean you have to ignore your brother. Continue to be kind and supportive and open to him. But I would not pursue his forgiveness as this is likely to be something he has to work through over time.