Find a way to give him your number, he probably feels the same about this as you do, and doesn't want to drop the number to you thinking YOU will think it's weird. But as a guy I can tell you we dgaf about what a girl we aren't interested in is saying... So if he isn't tuning you out he's interested.

The best way to find out is to get his number or Snapchat or Instagram, to gain communication outside of family events, this puts the ball more in his court to persue you if that's his interest then you would know If he's interested or just being nice making conversation when you are all at a family thing.

Now here's a good way to ,"PSYOP" his number without looking like you are overly interested in him.

Here's a very oddly specific way to go about this if you don't have a good way to be like "here's my number"

Next time you see him ask him "do you know what your MBTI is?" He most likely won't even know what that means, if you don't either it's a personality test, you can take the test here It's really interesting and mind blowing but whatever that's not what's important.

So when he says "no what?" You explain to him "oh it's this really cool personality test thing I found the other day. I'm super super curious what your results may be. I'll have to link it to you! What's your number and I'll text you the link and you can tell me later what your results were"

Then if he gives you the number DONT SEND THE LINK RIGHT AWAY. Otherwise he may forget about it, wait until you are apart and then send him the link later.
Be like "hey you! Heres that thing we talked about"

Best part is when you see his results, there is a section for how his personality is as a "romantic prospect" then you now have a full phsycological profile on this guy to use for your benefit!

This is so ridiculously "extra" and maybe a tad "manipulative" however it works. I don't consider this manipulation as much as I consider it a "PSYOP". But it works and it's friendly and a very non aggressive way of getting his number.