There should be a small push button on the breaker. Push it. if it clicks it was tripped. For your set up. I would operate under the assumption that the 12V aux from the TV will keep charged batteries charged if a few small things are on. It will not recharge a dead or very weak battery especially if inverter is running fridge. If you use the generator to recharge the batteries, hook the TT to the 120V out of the generator and allow the converter to do the charging. While charging, check the battery voltage it should be 13.8V or higher when convertor is running. The 12V battery chargers on most generators are marginal at best.
2015 Freedom Express 248RBS
TV 2015 Silverado HD2500 Duramax
TST Tire Monitors
Honda 2000I + Companion
2 65W solar panels