1976 Dodge Mobile Traveler - living space electric

Are you sure your house battery is any good? If your positive its good, then start at the battery plus and follow the wire. You should find a fuse, likely 30 or 40A and check it.

donn0128 thanks, I will try that. So if the fuse and connection are good, I shouldn't need to turn the ignition key to use the lighting?

House and chassis electrical systems are usually separated. There is often a solenoid controlled by a switch on the dash area, marked as emergency start or something like that. It is supposed to keep the two systems separate under normal circumstances and allow you to connect both as a means of jumping the engine should your chassis battery be too weak. See if you can locate that switch, or has someone disabeled it.
There is also an isolator which is a unit that allows some electrical power to be fed into the house battery when the engine is running. Those systems in the 70's were not the most reliable, you may have some tracking to do to find that box.
The way to start is to check voltage across the house battery. Then start the engine and check at the house battery again. If it has not changed upward, your system is not charging and could be the isolator or an open citcuit.
Other than that your best off breaking out a voltmeter and manually checking for electrical drains.
Grounds are the most common open connection. and must be very clean.

You will likely have plenty of oppurtunities to get familar with those systems so look at it right now as basic familarization, and yes you will use what you learn later.

Several useful suggestions
However, the key in the statement is the key must be on

No RV i have ever seen required this , as factory wiring

Somebody has altered the wiring, there might be a lot more that does not work unless the key is on
Fridge? Heater fan? Water pump?

Splicing mains power to ignition would not be too hard
But breaking out the light circuit from the house fuse box and connecting that and only that to the ignition would be a lot more work

Over 40 years, who knows what's been done, or by who. I would suggest you have a mobile tech check everything out. It sounds like you are stumbling around in the dark, literaly, and could cause a bigger problem.

"The key must be on" implies to me that the isolator is engaging and you're using power from the chassis battery only. Often the isolator setup is just a high-current relay (or solenoid--different name for the same device) that is actuated by the run circuit of the chassis so the house battery is connected and charges while the vehicle is running. Often there's also a pushbutton switch to turn it on labeled emergency start or something similar, to provide juice to the chassis from the house battery should the chassis battery be dead.

Your house battery is either bad or it's not connected for some reason. Verify that the cables to it are sound and the connections well-made. Don't forget to check the ground side as well as the positive side. Since it's affecting basically everything, it should be something fairly close to the battery.

There's often also a house battery disconnect switch (often using a remote controlled latching relay) for most or all of the house electric system. While I would not generally expect it, it's possible that the connection to the isolator and thence the chassis 12V system is on the house side of this disconnect rather than the battery side, and it's simply turned off or not working.

Maybe you can contact the Mobile Traveler company in Junction City, KS for some help. I did some searches and spotted this thread out there...
Some history...
Looks like they were sold to someone who created a new company know now as Horizons RV in Junction City, KS. I think they're right off I-70.
Rebirth...

It would certainly be a long shot, but someone there might be able to help you out with finding old manuals or wiring/other diagrams, or maybe put you in touch with someone who built or worked on these things back then.
Good luck with it.

Is a lack of diagnostic tools or basic knowledge working against you :)?

You need to test with a meter or test light. GOOGLE "How to test a 12 volt electrical circuit"

MEXICOWANDERER no, I have a pretty good knowledge of electrical and mechanical stuff, I just like to get some background knowledge about what the problems could be so I don't start from scratch and waste a bunch of time.

How are the waves in Michoacán right now?

Chances are there is a switch - every rig I have been in has one - location varies. Sometimes in drivers section - sometimes near entry door.