The indicator light stays on our PVS50 water heater.

It sounds like the heating elements are getting coated with calcium/lime/other chemicals that are found in your water. This would indicate that the elements are approaching the end of their life and may be getting ready to burn out. Consider getting some new elements soon and scheduling a time to install them.

If the pilot light will not stay on, I suspect a bad thermocouple

Define the problem.

Robert Shaw water heater gas control valve?
Copy following link for replacement of each type of gas control and related troubleshoot.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

1) Copy following link to troubleshoot by type of gas control valve:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

2) Replace gas control valve.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Possibly the air intake located at bottom of heater needs to be cleaned with feather duster under water heater.
Read your product manual for steps.
Copy following link for general illustration.
http://waterheatertimer.org/images/State-select-air-intake-400.jpg
http://waterheatertimer.org/pdf/Flame-Arrestor-Screen-Cleaning.pdf
Other causes can be bad intellivent gas control valve, poor venting, hot attic, low gas pressure, dirty combustion parts, tripped FV system.
Copy following link for available intellivent troubleshoot resources:
The service manuals are large files and open slowly.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Google,put model number into search followed by " user manual " , should help you find the instructions.

Don, if you have done this before go for it. If not call a pro,you will thank yourself later!

I actually just installed one of these the other day, I found that the ignitor wires were straped to the gas inlet and they were shorting out,, I wraped them with electric tape and the unit came on and stayed as for the thermostat make sure your flue is clear of all obstuctions even outside, make sure on the vent on the top back of the unit is clean and no lint or dust has built up on it, you can take a small soft brush and just sweep it across it