IPhone 11 will not STAY connected to the Bluetooth radio on my Toyota Tundra

We have two new iPhone 11s. iOS:13.2.3

We paired both phones to the sound system in our 2019 Toyota Tundra.

Both phones successfully paired but within 2 minutes the sound system shut down. The sound system then restarted. It then shut down again. This continued until we unpaired the devices from the sound system.

Today (12/3/19) I took the truck into the dealer. They updated the sound system software/firmware. I attempted to pair my phone again. The problem persists, the phone connects but almost immediately the sound system shuts down and restarts. The hands free phone is unusable.

Tonight, I chatted with an Apple rep. The transaction did not get me closer to a solution. To say I am dissatisfied with the service I received would be an understatement.

i am hard pressed to believe that I am the only one with this problem! Is there anyone in this community with an idea that will work?

post script: Toyota will replace the radio (still under warranty) but I do not believe that this will solve the problem. A new radio is likely to have the newest software/firmware installed that I got today.

one last note: we had two iPhone 10s that worked with NO issues. Time to take the iPhone 11 back?