Based on the symptoms you’re stating, I’ll posit a guess or two:
1) Since the solenoid appears otherwise operable when not connected to the house battery, I would look elsewhere…
2) Do we know if alternator of sufficient current capacity to charge both the truck and the house batteries??…Voltage will normally drop off under a more severe load – house battery is the load, so I’ll assume a yes…
3) No mention of a failing fuse (to 7 pin power terminal) inside the under hood fuse box – fuse seems to be ok as demonstrated by the voltage drop off when solenoid is connected to house battery. Voltage drop off suggest high current.
4) Disconnect the positive battery cable to interrupt charging to the house battery…Did the solenoid output voltage then rise??…If so, this suggest that the problem does not reside in the vehicle-to-camper wiring or the 7 pin connector cord.
At this point I would begin to suspect an internal short the house battery or possibly a short in the battery cabling…
JMO
Phil
