OldTrojan66,
From the measurements you have taken, it appears that your suspicions are correct and the truck's alternator is NOT charging the trailer's battery.. However, the shore power circuit is fine and charging the battery as it should. You've already checked the fuse, so that's a good start.
As I see it, there are several possibilities:
1) One or more diodes on the truck's alternator are bad, resulting in reduced output,
2) The truck's battery is bad with one or more shorted cells,
3) The charging relay is bad, causing the alternator output to never reach the trailer, or
4) You've got an open circuit in the wiring - either in the trailer or the truck.
If I were betting money, I'd go with #3 - relays fail for all sorts of reasons. The shotgun approach says simply replace the relay and see of that fixes the issue... but there are still some additional measurements you can make that will help to further narrow the possibilities.
Possibility 1): Bad alternator - This is easy to check. Fire up the engine and measure the voltage across the vehicle battery. If you've got bad diodes then the output voltage will appear low (since one or more AC phases will not be rectified). If the alternator output is low, then the truck's battery may not ever get charged sufficiently to trip the changeover relay.
Another "bad alternator" possibility, albeit considerably less likely, could be a bad ground reference on the voltage regulating circuit of the alternator that supplies current to the field windings- look for a small gauge wire coming off of the alternator and ensure that it is securely grounded. Most modern alternators have everything internal, so you may not see any wire.
Possibility 2): Bad truck battery - This is similar to #1 in that if you have one or more shorted cells, then the truck battery's voltage may not ever get high enough to trip the changeover relay. The changeover relay is typically a voltage threshold device that is there to ensure priority charging from the alternator goes to the vehicle's battery... any excess capacity can be used for other purposes. Verify battery integrity by simply measuring the voltage across the terminals, preferably an hour or so after the truck engine has been shut down in order to dissipate what is known as a "surface charge".
Possibility 3): Bad relay - The charging changeover relay is a switch that takes the output of the alternator and directs it to either the truck's battery or the "accessory" circuit (i.e., the trailer's electrical system). Although the check is fairly straightforward, the results may be somewhat inconclusive and require additional tests to be performed. The switching threshold voltage could be just about anything from 13.6 Vdc to 14.5 Vdc... or even more. This depends upon the design threshold voltage, the age of the relay, and the integrity of the connections... especially the reference ground. Hopefully, you can visually inspect the relay outputs and determine which goes to the alternator, vehicle battery, and trailer.
Have someone start the truck while you have your head stuck under the hood. Did you hear a click soon after it started? Good - that's probably the relay switching the alternator output over to the trailer. Measure the relay inputs/outputs - one output ought to match the input (i.e., alternator output) fairly closely, while the other output will reflect that battery's present voltage.
Is the input voltage somewhere in excess of 13.6 Vdc and the accessory output of the relay active? Good, the relay is working properly. No? OK... inconclusive. But if the alternator output voltage is high and the truck's battery voltage is high and it hasn't switched... probably relay or relay connections. Measure the ground leg of the relay with respect to chassis ground (i.e., some heavy steel component or the vehicle's battery ground terminal). NOTE: At this point, you may want to simply "pull out the shotgun" and replace the relay... assuming it's not too expensive.
Another approach that you may want to employ as you attempt to isolate the problem to the relay is to hook up a battery charger to the truck's battery and let it charge the battery above 13.6 Vdc - typically that's the threshold voltage used to switch the relays.
Possibility 4): Bad wiring and/or interconnection - As TucsonJim suggested, disconnect the trailer from the truck and with the truck engine running, measure the output at the trailer's electrical connection. Pin 1 = Ground, Pin 4 = 12V. If you've got alternator power output there then you have a wiring issue. NOTE: It could still be a high-resistance issue in the truck's electrical harness. Much more testing will be necessary to fully isolate the fault, although there are some high-percentage possibilities that can be looked at first.
Good luck.
