The "T" is just trim, designed to finish the gap between the 2 adjoining overhead panels. It's not designed to carry much weight at all. I sounds like maybe the contact cement between the headliner material and the luan above it, or the luan itself to the foam/roof structure above it, is letting go. In either case a careful repair is possible.
Worst case is the possibility you have a water intrusion issue causing that luan to delaminate. There, you could be in trouble as once the luan has started to delaminate it's generally due to rot. This will be a much more involved/expensive repair involving repair of the roof leak, and the replacement of that sheet of luan.
In either case, I would encourage you to get the repair done ASAP as it's not going to get any better by itself. If left it will almost undoubtedly get worse.
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1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake
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