I'll just add I had a not the same but similar issue on the silverado, really screwy electrical issue the radio would cut off and on, cluster would flicker, heater would turn on/off, tons of errors like brake error, service this/that errors. etc
tried dam near everything one could think of to fix it, dealer even replaced the cluster and pretty much could not find the issue.
I finally gave up and told the dealer to put there best tech on it and don't call me till you find it.
took the tech2 about 2 hours with a oscilloscope to find that my alternator was throwing 800ma electrical "burst's" and this was causing the bcm to think the ignition was being cycled and just causing all kinds of havoc.
not saying your issue is the alternator but it might take a scope on it on various sections until it is found.....
if that electrical short is faint enough you might not see it with a regular meter