As suggested above, turn on your LP tank, purge with the gas stove, and then turn on the gas for the water heater with the switch. The red light should turn on for about 15-30 seconds and then go off. It turns off once the propane fires at the water heater. (normally it does anyway)
If you flip on the electric and things are quiet, you can hear the water beginning to heat up. But, things need to be quiet, no air conditioners running, no electronics blaring, and no dogs barking or kids screaming. Put your ear as close to the outside of the water heater as you can and you should be able to hear a slight humming/hissing sound (very, very faint). If you do, it's heating up. It will take about 15 minutes before you feel the warm water. It will take about 30 to 45 to heat the tank completely.
On mine, I have two lights to indicate if the water heater is on, one for electric, one for gas. My (blue) gas light does not shut off. It stays lit all the time. My previous campers, that light always went out once the water heater fired on gas.