I have had the same issue here, for the last 2 months. First few glitches that were solved by restarting the phone (did not feel so different from the classic random reboot issue…)
It got worse quickly, and for me it has become obvious it was linked to heat. As the phone is prone to overheating, I am now convinced one chip got damaged with false contacts somewhere. Twisting the phone sometimes makes the screen working, but nothing permanent.
I feel that only replacing the core module would (maybe) work, but I don’t think it is worth it anymore on this phone : I would have loved to keep using it for several years, as everybody here, but a brand new recent phone is much cheaper, and my FP2 lost a bit of my trust after 3 years sometimes painfully owning it…
Just giving my feedback on the glitch, no real solution to share, sorry to say…
EDIT : applied the workaround from letrollpoilu, placing a filler between the case and the phone to put pressure on the pogo pins connecting the screen. Worked for some days, but now it is back to before, or even worse (I guess it forced on the pins that got broken further…).
In contact with the helpdesk, the solution is to change the full core module, so to expensive for me.
So I am out, buying another phone, see you for FP3 maybe!