Update on solving the fresh water tank slowly filling when not selected (when connected to shore water):
First, the old fill valve was indeed defective, even after complete disassembly and cleaning. I can blow air through it when it is supposedly closed. I already posted the solution for that above.
Second, the water pump was ALSO back feeding into the fesh water tank when on shore water. I have the Pentair Shurflo 4008-101-E85. The 4008-101-A85 is identical but sold to RV builders, while E model sold to consumers.
I dissasembled the upper housing which looks like this: Amazon.com: SHURFLO 94-800-00 Model 4008 Complete Upper Housing : Automotive
8 screws removed, then the 3 screws on the lower left. Pay close attention when taking the cover(s) off of what goes where. I expected some debris or corrosion with the check valve, but none found. Cleaned anyway, re-assembled and now no water pass though to fresh tank (so far)
I plan to get a spare check valve, either inside the pump, or inline on the water line (suction or pressure side).
The 4008 pump check valve has changed over the years. Ordering only the check valve will not work unles your pump is build date newer than approx 2020 according to many reviews. So it will not work for me. Check valve: Amazon.com: SHURFLO 94-800-03 Model 4008 Repair Parts - Check Valve : Automotive
Instead, the complete upper housing must be purchsaed, and it includes the new design check valve, and includes the pressure switch. Amazon.com: SHURFLO 94-800-00 Model 4008 Complete Upper Housing : Automotive
Shurflo sells a inline check valve, but it is plastic and several reviewers say it failed and spewed water. Amazon.com: SHURFLO 340-001 in-Line Check Valve : Tools & Home Improvement
If I go the external check valve route I will buy a metal one way check valve, 1/2" barbs, with clamps.
Other option, buy entire new 4008 pump, approx $65 - $75 on line by shopping around, then keep old one for spare parts. A new one "should" have the new design check valve.
So far the probelm is solved, but I expect the water pump check valve to hang up again in the future.
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