12.4 is not dead, but it's about 60 percent discharged. The information that sticks out though is you get 12.4 at the battery when the generator is running. That sounds like you still have a battery shutoff switch or a blown fuse. You are probably going to have to start tracing wires from the house battery to the inside. As bobndot suggested focus on the grounds first.
Leave the generator off and the shore power unplugged. Use your meter and measure the voltage between the positive and negative terminals of the battery. This is your battery voltage, write it down somewhere. Every voltage check you take below should show very close to battery voltage.
Remove both ends of the ground wire, clean off any rust and reconnect. Check voltage from the battery positive to the frame mounted end of the ground.
From there start following the positive wire. Look for any old circuit breakers or fuses. Once you find one use your meter to check the battery voltage on both sides. On a circuit breaker you can connect from each post one at a time to ground. You should get the same battery voltage on each post.

If you find a fuse you can poke the positive lead of your meter to the slots on the back of the fuse. You should get the same battery voltage on both sides of the fuse. If you get voltage on one side but not the other, the fuse is blown.

Edit: Wait, an RV that old probably has glass fuses. If glass, then measure the voltage from each metal end of the fuse to a good ground.
If you can't find a bad fuse or breaker then start looking for the fuse\breaker box. Not sure on a rig that old, but I imagine it's a small panel with a door (probably metal) mounted on the wall somewhere in the living quarters. Find that door and firmly turn every breaker and then back on.
Now see if you can find a good enough ground to check both ends of the fuses. I'm assuming they are glass fuses so just measure from each metal end to ground. You should get the same battery voltage reading on all fuses.
If you do not get battery voltage, or you see some abnormally low number then you have a switch or blown fuse between the battery and the fuse panel.
If you find close to battery voltage at the fuse panel then start the generator and measure the voltage at the fuses again. With the generator running you should be seeing a number higher than battery voltage.
If you have higher voltage, then start tracing back toward the battery until you find generator voltage on one side of a fuse or circuit breaker and battery voltage on the other side. Fix or replace any component that shows a difference between the two ends.
Good luck and come back and let us know what you find, and we'll have more suggestions.