The 12V television in our Solera is hardwired into the 12V system (No cigarette lighter plug). If your TV works when plugged into shore power and the battery disconnect is OFF, then it's a 110V, if not plugged into shore power and it works with the Battery disconnect ON (and inverter off if you have one), then it's a 12V. At least that's the way it works on my coach.
12V TVs use less power than 110V, hence they are more user friendly when dry camping
- (works without having to turn on inverter) - which also has a parasitic drain on the battery.