It says you can use any thermostat "suitable for 12 or 24v systems" so IMO be a good idea to replace it.
I have had to replace the water heater propane switch that has that red light on it in the 5er. Those switches wear out but can work sometimes first before not working at all. Hard to tell if it the switch or the actual ignition etc. Switch is easy fix. Same as the other thing, jumper the wires to it to see if the thing then works.
The MH, has the monitor panel on the range hood. It had 12v ok for the water pump and light, but no lights for the levels. Needed a new "momentary" rocker switch in the panel. Easy to pry the panel out from the range hood front to get at it all. It has a level light for the big propane tank, so we'll see if it is telling the truth about that level. No red/green indicator like before with the two 30lb tanks in the 5er.
The MH came with a 6300 converter. I did the fuse panel jumper trick and by-passed the 6300 converter part to use a newer type deck mount converter that does not need a battery to act as a filter.
I have not got the television antenna working yet. It is a sort of weird batwing but has no amp in it--the amp is in the wall panel. The panel has 12v ok but the amp seems dead. Anyway, I can see a Jack going in there soon. :)