Estranged from sibling…want reconciliation (delete if not allowed)

Hey all, so I’m on the opposite side of many of you. I (30M) was estranged from my brother (33M) officially about 3 1/2 years ago but I’d say unofficially for over ten years. His primary issues was with my mom and due to poor communication within the family, I got caught in the middle of it all. I thought it was something that I could personally help fix and first it wasn’t my business and second it’s not something I could fix. In doing so, I believed my brother hated me but I think he was rather hurt by me (I was an asshole teenager). So he wanted me to show that I cared for him and I didn’t know what that meant. Fast forward to today…I’ve since gotten married and now have a son of my own. I’ve grown a lot in the past couple years and a lot since I was a teenager. I’ve respected his wishes of no contact. He actually has talked to me on two different occasions (once at a wedding and then at a funeral) and he brought all my legos back (his own doing) which was a nice gesture. For contrast, he won’t say a word to my mom. But me he will and will interact if we are in the same little area (he doesn’t seek it out and neither do I). My relatives who do talk to him have all said that he (my brother) has said that with time him and I can have a relationship and his big hold up is that he’s worried I might drag him back into issues with my mom (zero desire to do so!!!). Id like to reach out to him…was thinking a letter because it eliminates the casualness of a text and to me it shows more care because it takes longer to send, plus a phone call is too demanding. Is this a horrible idea? Again, delete if not allowed. Thanks

TL;DR: want to reconcile with brother. Have been respectful of his wishes. Have had good interactions with him since and apparently he does see a future relationship. How do I proceed/let him know I’m also interested in that?