bklaes

Again, Tom Cherry comes through with great advice. 
I unplugged the Norcold's ice maker and the GFCI has not tripped in 16 hours.  I'll plug the ice maker into the same receptacle as the refrigerator.
I regret and apologize that I didn't search for my problem on here first. 
My thought was, this is so weird, I doubt anyone has ever seen anything like this before.  I was wrong and will do better next time.   
Thanks to all that helped me through it.  

Good News.  Problem solved.  Very low tech.
When any of the three S/O buttons on the system panel was pressed, I could hear a faint buzzing coming from the Slide-Out Relay Module box, located in the battery compartment.  I unplugged both of the Molex connectors, sprayed with DeoxIT, then reseated both and all is well again. 
Thanks to everyone who chimed in.