Cannot seem to win with this bluetooth thing.
A couple of years ago I replaced the bluetooth module with a used unit sourced from a US auto wrecker. Mine was drowned and corroded by the usual water problem, although in my case it was condensate from the a/c drain rather than the usual sunroof drain leak; same result though, rusted out bluetooth module and central infotainment screen cycling on & off.
After replacing the bluetooth module I again had problems with the infotainment screen cycling on & off, when this happened it seemed to be random chance whether the phone would connect or not when the screen came back to life. Several times I cleaned the electrical and optic connections.
A few months ago I had a current drain problem which I traced to the NAV module not shutting down (could hear the cooling fan running continuously); this NAV module is also on the fibre-optic loop although it is located way back in the left side of the boot / trunk. I disconnected the wiring harness to the NAV module and bypassed the f/o connection with a loop. The 'navigation' option on the central screen is now greyed out, no big deal as the system was way out of date anyway.
Since then I have not had the screen shut off at all BUT I have also not had bluetooth connection at all in this time.

Earlier this week I was in a suitable mood to fiddle with jaguar electrical gremlins like non-rotating vents, non-working door locks etc, decided to again fiddle with the bluetooth module to see if I could get connectivity back. I lifted the seat and carpet, disconnected and reconnected the electrical and f/o connectors from the BT module. BT connectivity was restored and after pairing the phone all seemed good.
This morning I drove the car for only the second time after doing this; on startup, the BT icons were there, all good; after about 2 minutes the screen started the old on / off cycle again, continuously.
Of course this means not only no phone calls but also no radio, no seat heating / cooling, no climate control. Worse by far than just no BT.

I've looked online for another BT module and they seem to now contain gold or diamonds- prices around US$400 for a used unit (none came up in Australia). I paid around US$80 plus shipping for the one I currently have.

I'm about ready to give up on this but I HATE having something not working and it is ridiculous with a 'modern' car to not have the phone connected. Seems if I disconnect the BT module it will solve the greater problem of the screen cycling on / off but this is not a fix.

Hs anyone found a proper solution to this problem?