If it uses the sender on their website it is a standard 0.5-4.5 volt analog sender, so where does the 5volt requirement come into it?(rhetorical question).Batter is 2 year old Delco and healthy (12.8 V; 14.1 V charging).
Gauge/controller sends I believe 12v to sender which returns 5v (decreases with boost) tech support says initialization is highly sensitive to the gauge getting 5v signal when cranking.
An interesting puzzle for us but a big PITA for you. I would theorize the 12v supply is dipping when you start and causing a initialize/reinitialize and the so called 5v sensing sees something a bit off. I can't think of a real easy "layman friendly" way to test this theory, powering the gauge from a regulated wall wart/ another battery?
What is the actual cranking voltage?