Hello "Country Gentleman". I also have a 2003 Safari Cheetah, and do all my own maintenance. As an aside, you don't really have a Cummins engine - it's a Caterpillar. That's not pertinent to the problem, though. Tim had good advice for you. To clear up the "exciter wire" thing, that wire is actually not an exciter wire, but rather a remote voltage sense wire. The alternator will adjust its output voltage such that the voltage wherever that wire is connected will be 14.7 volts. It is supposed to be connected to the positive connection of the chassis batteries (or a point that is itself connected to that). Monaco/Safari ran that wire to the isolator and connected it to the post of the isolator that goes to the chassis batteries. That wire, and the one that feeds the "ALT FAIL" light relay, are often subject to corroding and breaking where they connect to the alternator, either of which would give an "ALT FAIL" light. In your case, the remote sense wire could have broken anywhere, maybe at the isolator. As long as you now have a good connection from the alternator remote sense post to the chassis batteries or isolator, that problem should be fixed.
As Tim suggests, the best next step is to identify if there is a current drain from the chassis batteries, and if so, where it is. I use a multimeter that can clamp around a wire to read the current flowing through it. The most common version of this "clamp-on" ammeter reads only AC current, but there are (more expensive) models that also read DC. If you can find someone with one of these, you can identify which wire leading from tube battery is carrying the unwanted current, which should narrow the possible culprits.
Someone mentioned the inverter, but your inverter does not connect to your chassis batteries. I would check the isolator. With the engine running and batteries not significantly discharged, you should measure one voltage (around 15.5 volts) at the center connection (the larger one that comes from the alternator, not a smaller voltage sense wire), and about 0.7 volts less at each of the other two connections (chassis and house battery connections). With the engine off, the alternator connection should read zero and the other two should be around 12 volts or so.
Bill Halberstadt