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GPR is a relay for switching 100 amps.
Contacts burn out with age and coils can go bad over time once insulation breaks down
low voltage can cause the contacts not to engage fully and then burn them out
some times it can be just a corroded connector or cable lug
Stancor makes a better relay, I have one for a spare
Its a E350 7.3 think its a hard replacement
Should I hear it cycle
Take the cover off the dog house, you should be able to hear it click. On a F series the relay is located about midway down the engine valley on the passenger side. I assume it would be located in the same place on the E series.
I can hear my Stancor click. Swapping to it was one of the first things I did on my truck. First were new batteries (850CCA), cleaning grounds, and a Denso starter.