You should look in your battery control center.
On my rig, the charge relay and the auxiliary start are the same relay.
The switch on the dash should be connected to the same terminal that comes from the circuit board in the battery control center. The other side of the switch should be hot from the battery control center.
I went through a couple relays before I was able to seal a new one up. I got the current one from NAPA many years back. The small terminals corrode inside the relay causing it not to energize. Make sure you get a good continuous duty relay of at least 100 amp rating.
I used standard silicone between the two parts of the metal can to keep moisture out.
Your generator issue is most likely a corroded connection somewhere in the circuit. It could be a ground connection or the positive. Use an Ohm meter to check each connection. Use a voltmeter to check for voltage loss.