Yeah, shop manuals are priceless when the need arises. Really a must-have item with any old vehicle if you're going to do even the smallest jobs yourself.
And once all the wiring is determined to be clean, tight and in good condition, the book tells you how you can adjust the old regulators to work better, as was said.

Because it's adjustable, that means that it can come out of adjustment. And chances are it's never been touched and tweaked since the truck rolled off the assembly line!

It was a good thought thinking it might be a wiring issue. But as you found out, it's normal.
Every vehicle from probably the thirties (though I don't know that) all the way through most vehicles today, have certain systems fully functional without the key. Those would be headlights, brake lights, dome lights, hazard flashers, and horns.
All can be critical safety concerns if they don't work all the time. But it's also why we have to remember to turn the lights off or it'll drain the battery.

It was only later after more and more computer controls came into play in the nineties and 2000's I think that we started having the car tell us it knew more than we did, and making us turn on the ignition to keep the headlights on. Many modern cars will turn them off even if you put the headlight switch in the full ON position.
Annoying to people who like to tinker with things without a warning buzzer telling you that the keys are in the ignition and the door is open!!

Paul

 

What I meant to add to what the others said about checking the wiring, is to always remove and re-install glass fuses in the fuse panel when doing an inspection.
Surface resistance builds up over time on the contact surfaces, so the act of pulling the fuse out and then putting it back in can break the crust that you can't even see, and help the flow of electricity. Making everything work easier.
Old vehicle contacts can do this. Fuses, connectors, wire ends, etc. Becomes part of your normal maintenance rituals every year or two.

And when a BAT light starts to come on, put a volt-meter right on to the battery terminals to see what it reads. If it's above 13.5v or so there is probably some resistance in the light circuit. If it's under 13v or so, your generator is not able to charge efficiently.

Paul