Even though it's frustrating, I think it could be useful to discuss your thoughts about why a no would be so disappointing and how it would affect your relationship with your T. Also how a yes would affect your relationship with T. Basically as a way to open up that by you doing me this favor it means XYZ because of ABC.

Basically discussing those complicated layers as you say could be very useful. After that I think it would be good to ask the favor. Then perhaps a no wouldn't be as impactful on the relationship. Also perhaps you could somehow get what you need from T on a different level without the condition of T dong that particular favor.

Having said that sometimes we just want a favor from someone for the simple reason of wanting that thing and nothing more.