As a disabled parent, I get the frustration of knowing it would be so easy for teenager to help with X when it's such a pain for me, but they're not helping or getting them to help feels like I'm being a burden to them with the way they act.
On the other hand, no, I don't think he's automatically being a brat for not being ready and willing to help whenever requested even if he doesn't appear busy to you. I get it feels that way, I've had that gut punch overhearing 'what does she want now?', but I have to remember that my kids are allowed to be tired too. To be in pain too. To not be arsed just as much as I am. To have different priorities and not see things my way.
I 100% agree in having a conversation around everyone participating in the household and helping each other and how to help that go more smoothly, but don't go in with him being the bad guy. With my 17 year old, I find discussing what and how he's doing before asking whether he'll be up to X later works far better than saying 'could you quickly...' at the moment I could use something. Sudden transitions and teens tends to cause issues in my family when if I give them my ear for a few minutes and then wait 5-10 minutes to finish something up, I usually get all the help I could want and more.
The older mine get, the more I find that discussing it in advanced and not assuming they're ready to help just because I can't tell they're busy makes things go a lot smoother and our relationship a lot better. We have a lot of discussions on what we all need in the upcoming days, what we want to do and balancing how we can help each other. Being proactive means I feel hurt a lot less, and it's the very thing I want my kids to be. Sometimes urgency is needed - I've had a lot in the last week having an injury resulting in not being able to carry much at all - but if I make everything urgent, what's actually urgent tends to not go as well.