If the bulb checks out, it might be the relay under the dash for this circuit. It switches the back battery on with the key, since the key switch is all 12 volt circuits, this relay is what controls it. The front battery(gen 1) lamp is switched by the key switch.
I found one relay to have corroded contacts. This is a 15 amp relay, using it for the low current demand of the gen 2 light may prevent self-cleaning.
Don't confuse this relay with the voltmeter relay. They are the same, you could swap them to see if that helps.