Quote: When the engine is running, generator off:
14.4V is read at the center post of the isolator and at the starting battery.
12.28v is read at the other post of the isolator and at the deep cycle battery.
Your isolator is defective. You should only have a .7 volt difference between the center post and either of the outside posts. Using a voltmeter with the wires off will fool you. Without a load on it you not get an accurate reading. To demonstrate that just put one lead of your voltmeter on the negative battery terminal, hold the other lead in your fingertips of one hand and then touch the positive side of the battery with the other. The meter will show voltage. Not enough current flow to feel or drive an electronic device but enough to drive a meter.
Re-reading the voltages leads me to believe the previous person had an issue with the isolator and bypassed one section already. That is why you have the full alternator voltage on the starting battery. Could be they are now trying to use the solenoid to tie the house battery to the starting battery.And you said that in your last post. So as you suggest, finding the lost 12 volts could be as simple as a blown fuse.
You could replace the isolator but finding the missing 12 volts should be an inexpensive fix.
H/R Endeavor 2008
Ford F150 toad >Full Timers
Certified Senior Electronic Technician, Telecommunications Engineer, Telecommunications repair Service Center Owner, Original owner HR 2008