A quick way to test is to use a DC VOLTMETER on the battery terminals without shore power or generator running. If the battery is fully charged it will read 12.6-7VDC
Then start your truck motor and if the Dc VOLTAGE across the battery terminals jumps up to 13.6VDC then this will be telling you the truck alternator charge voltage is making it back to the battery terminals...
If it doesn't show an increase in DC VOLTAGE then start looking for some of the things said above...
In my case I had to install a RELAY and a FUSE that in my truck glovebox in an unmarked envelope. In the truck manual these items were identified as trailer tow fuse or tow relay or something like that.
However don't get too excited as in my case the charge voltage coming from the truck alternator would give me 6 amps or so of DC CHARGE which is great to have but will not re-charge a battery very quick. It is more of a top off charge.
Roy Ken