I looked for the schematics for voltage monitors, but couldn't find anything "generic" There are a couple of brand specific connection instructions, troubleshooting instructions, but not knowing what you have installed, didn't persue any further.
Now, in response to some of your observations:
ie: Fan on converter running at times.... etc. When the trailer is plugged into shore power, the converter will provide 12 VDC electrical power (up to it's rated capacity) and in doing so, it generates heat. The fan will come on to provide cooling air to the converter to prevent overheating. It is designed this way and it's normal for the fan to run when converter is "making 12 volts". The fan won't always come on with the same number of lights because as it charges the batteries and provides for other electrical requirements, the amperage will vary and the fan comes on based on total output, not necessarily just the lights you count as a "load".
The fan should NOT come on when the shore power is not plugged in. In this scenerio, the batteries are providing 12 VDC to run the trailer and the converter is not used, so it is not generating heat and the fan should not come on. If it does come on, something is wrong.
As for the indicator lights going out as you turn on lights, I believe most indicator panels use a LM339 Low Power Low Offset Voltage Quad Comparator IC to sense the battery voltage and light the LEDS. As the voltage drops, the lights go out sequentially, indicating "lower voltage" in the circuit. If the wire is too small on the circuit being monitored, you'll get a voltage drop with increased with increased load (turning on more overhead lights, etc). This would give the voltage comparator IC the indication that voltage is dropping, when in actuality, the voltage is still 12.6 VDC (or close) at the battery, but the available voltage in that particular wire is lower because of the excess use. You may be able to just relocate the monitor wire from where it's connected to the + terminal on the converter/battery connection and get a more accurage reading. Some monitors have potentiometers that can adjust the LEDS, but I don't think the inexpensive ones used by Keystone have that feature.
I'm still pretty much convinced that you've got a ground corrosion problem, or a + battey supply connection problem somewhere in the wiring. Something in a connection somewhere is not allowing full amperage to flow.
Since you've got it "sort of working" for now, I'd monitor it and enjoy the camper. To test the ability of your batteries to provide energy for a camping trip, just unplug your shore power, leave your lights on and turn on the furnace, go about your business and throughout the day, check how things are running. When you notice the lights getting dim, or the furnace not running as fast, measure the voltage at the battery and see how far down you are. Once you drop to about 11.5 VDC, record the time from start to finish. That should give you an indication of how long you can dry camp with that amount of electrical drain. If it's over 5 or 6 hours, I'd say your system is operating pretty normal since you won't normally be using that amount of lighting or that amount of heat.
As you find time, keep checking, cleaning and tightening the circuit connections. You may well have a twist cap connector somewhere that's not twisted tight enough or that has some corrosion in the wire ends. Since it's the 12 VDC circuits and not the 120 VAC circuits, you don't have as much of a safety issue to deal with, so start your camping season