It is a defective circuit board. My Bigfoot truck camper uses the same water heater with electronic ignition as is in my motorhome (motorhome is 10 gal, however).
First I swapped the ignition probe; did not solve the problem. Next I swapped the circuit board: the furnace fired up immediately...ran until water was hot.
Thanks to Jeeperrmartin, David K, DancinCampers
I am going down to a local RV service shop to pick up a new circuit board.