I'm an honorary uncle (amongst other things, see below) to my friend's two children. I visit them once a month and spend the day with the two of them and they seem to really enjoy these visits.
My friend has recently gotten married and her new wife had a 13 year old child. The 13 year old's father is not at all involved in their life, while the biological father was not abusive himself his sister was and well suffice to say it wasn't a good situation. Anyways the point is the 13 year old never had a father figure or any male role model in their life. They also have had to deal with some other issues, including being non-binary and getting people to respect that, and has grown a bit defensive and unwilling to express their feelings, pretending to always be good regardless.
I suppose it's just relevant enough that I also need to bring up how I became an honorary uncle to the other kids and hope people don't get too distracted by it. I also donated sperm for my niece to be conceived - and thus am technically her biological father, though we try to avoid using that term so as not to confuse the kids. All kids know I'm the girl's sperm donor and I try very hard to be equally an 'uncle' to both kids not just the one I had the honor of donating sperm for, the younger two don't seem to care too much about the sperm donation and are happy to have me as an uncle. However, the mothers have been working to have my friend officially adopt the 13 year old and during those discussions the teen has made allusions to me as the 'father' of my 'niece' - despite their mother's trying to convince them that I agreed to not be a father when I donated sperm and that I should be considered only a donor and honorary uncle - and made comparisons to their own non involved father in a way that suggests perhaps a bit of envy or regret that they never had a chance to have the sort of relationship I have with the younger two.
Anyways they have suggested to their mother's some interest in me during therapy, including referring to me as uncle and generally suggesting they would like to have the same relationship with me that I have with the younger two. I'm happy to be an uncle for them if they want it. The main problem is that they aren't going to come out and admit that they want that relationship. I have tried to tell them I'm happy to be their uncle but they blew it off with a very nonchalant attitude as if it didn't matter to them. I feel like I could, and should, do more then just tell them that, but I don't know what more I can do.
I should also mention that while we tend to get along well enough when we talk they often spend most of the time during my visits in their room, which is pretty normal for teens. I know that's pretty normal, but with my only getting once a month visits with the other kids and them only coming out of their room to interact for part of that time I don't exactly get that much time to interact with them. For the record the once a month visit thing isn't an estimate that's part of the agreement with my being a donor and so I can't just increase my visits. I could probably do a separate day just with the teen without breaking the rules about how much contact I get with the younger kids, but the teen is never going to admit to wanting contact enough that it wouldn't feel odd for me to suggest a one on one day together, nor do I know what I could do on such a day; especially considering I'm really cheap - with good reasons - and wouldn't be able to pay to take them to any expensive activity they might like.
So my problem is how to show them I mean it and actually be there for them when they won't admit to wanting a relationship? What can I actually do for them that they would appreciate and value? I have tons of experience with kids, but I always have joked my expertise stops at teenagers. If they were a little younger I'd know how to get through their defenses and get them to open up, but I don't have nearly he same experience or capability of working with teens. I'd like to be available to them however I can, so long as it doesn't take too much time away from my other niece and nephew, but I just don't know what more I can do beyond telling them I'd like to be something for them. How can I give them what they want?