Ok. as the water heats first the T-Stat should open, this is normal operation, and burners stops.. The water than cools, the T-Stat closes and it "Recycles"
Page 2: IF the T-Stat continues to heat the ECO should open, this will cause the lock outs you cite.. but should not blow the TPR.
IF it continues to heat, a plug in the TPR melts, when this happens it does not drip.. IT GUSHES, I mean Niagra Falls level Gushes. (Been there, Done that, not on an RV though) I mean Gallons per minute, Not drips per minute.
Dripping indicates a need to drain and flush the water heater.. (Routine maintenance) LET IT COOL, Remove drain plug, Install short 1/2 inch pipe (plastic, brass or metal) to extend flow past side of RV, if Suburban needing anode inspect anode and replace if needed. Flush using flush want (optional) and once drained close TPR and replace plug.
But check the T-Stats.
It is doubtful (Impossible on mine) that the dripping TPR is dripping water onto a circuit board and shorting it out. But I am basing that on MY water heater.. I've not seen yours.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times
