I don't know how to put this in any other way. Maybe I'm an idiot and know nothing so ...grain of salt. I'll just put out my thoughts.
I think I handle my parrots very well because when I was traveling and couldn't have pets for a while I was addicted to Caesar Milan the "dog whisperer" when it came out like what 8 years ago or more...
You say the bird is bonded to your dad......the patriarch....the leader of his flock. He probably has that calm, assertive energy that just says I'm the flock alpha and come step up I want you to cuddle with me now.
I....would work on that. Be extremely calm but talkative and assertive. be the flock leader to your one bird.
(It may not even be a bad idea to have a play slap fight with your dad with you winning in front of the bird....(really might do nothing but you have to admit it would be fun.))
Anyways the birds can pick up on energy, or rather body language, and tone of voice etc. Make sure you establish yourself as the "parront". The more you are a leader of your flock and yourself, the more the bird will trust you and follow your lead.
At least seems to be in my case. When My birds get a panic, they jump and then 180 flap right back to my shoulder because they trust me over anything else in the house. more than their cage even.
That's my advice, take for what you will.....
Actually not bad advice at all, it's something that is totally worth trying, because if this is the situation with the OP's specific bird, where it is a "patriarchal" thing, then this might very well work...It's not usually how this situation goes, especially with CAG's, as they really do tend to be solely "one-person-birds"...I know we hear that phrase a lot used here and a lot of the time it has nothing to do with the bird being a "one-person bird", but with CAG's they really are very much "one-person" birds, at least in the sense that they typically have an extremely intense, strong bond with one person in their "Flock", who they choose for whatever reason they choose them, and then depending on the individual bird they may or may not tolerate certain other flock-members holding them/touching them, etc. (I don't know about Timneh's, never had much experience with them)...But it could be a patriarchal type of situation with his CAG, worth a shot for sure!!! I don't have much experience with men being around birds, my dad has never been a part of my life since I was 7, and my step-father is hated very much by my brother CAG, lol...He can't touch him at all. But it's the opposite situation with my brother CAG, he's always been around women only, from the time he was 3 months old when we brought him home until he would have been around 8 or 9 years old when my mom started dating my step-father, and even then they didn't get married or move-in together for another 10-11 years after that, so he just hasn't ever been around men...
I think the OP should give Clark's idea a try, you're both men and your CAG might very well have chosen your Dad as "his person" because he is the head of the household, head of the "flock", etc. So trying to take that role over for your Dad since you're always with your CAG now and your Dad isn't might just work...The only thing I will say is to be sure that if it's not working out and your bird only becomes more aggressive towards you, then once again, don't "force" it, like you don't want to force anything else....Take your cues from how your bird reacts to things that you try, and then keep doing the ones that he obviously likes, and stop the things that he obviously doesn't like...
****LOL Clark, I had to laugh about the suggestion of the OP having a "slap-fight" with his father...That might be the one thing in your advice that I would NOT try, only because there is a pretty good chance if the OP starts slapping or hitting his Dad in any way in from of his CAG, the CAG may very well attack the OP...You don't know, sometimes they will actually start biting "their person" that they are bonded closely to in that situation because they are trying to get them to move away from the "attacker", and sometimes they will ensue an all-out dive-bombing on the "predator" that is attacking their person...I'd hate to see the OP have this happen to him, ONLY because if it were to go that way where the CAG does get upset at him for attacking his Dad, that could make their relationship even worse and push the bird further away from him...Plus a CAG can do a lot of damage with their claws and their beak!!!