water heater and furnace troubleshooting

[rough road]

We have found a coach that we are interested in, all is good with the exception of intermittent operation of both the water heater and furnace.
The water heater is the typical 6 gallon, '05 and will not stay running, when cold it will start and run until the water is up to temp but once that happens it will try three times then go out on lockout. The thermo couple looks to be properly positioned, but the symptoms would seem to suggest that not enough voltage is being generated to keep the gas valve open ??
When electric is selected it start to sizzle like crazy but my thinking is that the element is simply coated with calcium or other minerals.....?

The furnace, same year, typical non ducted 15k btu? will also not stay running but will shut off once after the air is hot then go into a mode of constant attempts to start then shut down. It has spark ignition which looks and sounds to be strong and my thinking is that this could be a simple air supply problem, not enough movement over the heat exchanger and the furnace is simply going off on high limit BUT if this is the case it should restart once the exchanger cools down; thermostat ???

Want to make a fair offer but also need to protect ourselves.

I have the repair 'bible' but not enough tech info, suggestions ?

[Gary RVRoamer]

It does sound like it is cycling on the high limit switch. When it starts doing that, shut if off for 15 minutes to cool and see if it returns to normal for awhile. Better yet, switch it to fan-only mode if you have that choice - that should cool the heat exchanger quickly.

If that does it, then you probably have an air flow problem, either return air or output..