Do I really need the wire from the alternator to the bulkhead connector?

Thanks Mattax! I'll start with this, because I should have explained it:

I don't know what 1, 2, 3 represent but I would think any circuit on a relay can be fused or have a circuit breaker.

What pulls 120 amps!? Is there a winch? I would think that would be a big wire, like a starter cable 6, 4, or 2 gage.

1, 2, and 3 are PAL fuses, which are essentially fusible links. The #1 is the main fuse between the alternator and the battery that you can see in the image of the relay box in post #10. Ha ha, hopefully nothing pulls 120 amps! The wires on either side of that 120 amp fuse are really big, probably 2 gauge or bigger. 120 amps might have been OK for a 2nd gen Ram, but it makes sense for the old Swinger so I'll replace that with something smaller, probably 80 amps. Numbers 2 and 3 will be one of the other fuses in the relay box.

There needs to be a route to the key switch with power. Or to put it another way, the feed to the key switch has to be hot at all times.
So thats a line the should have a fusible link or maxi-fuse.

Right, that's the wire that's using fuse #2. It would be coming from the relay box (which is also a power distribution unit) and hot at all times. I would run it through a fuse, not sure of the size but it only needs to power the interior lights, side markers, taillights, radio, cigarette lighter, and starter relay trigger. I was thinking 30 amps.

The wire on fuse #3 is from the relay box to the starter relay. As you know, the factory setup would have the starter relay connected to the power cable coming out of the bulkhead. The starter relay fuse on the Ram was 40 amps, but I will probably start with a 30 and see how that goes.

The more questions you ask and the more I explain it, the more I think it will work. The only thing I'm not 100% sure about is whether I need a power connection coming out from the bulkhead to the starter relay (or to the relay box, since I'm already powering the starter relay via the relay box). Is it also required to power the ignition switch, along with the wire on fuse #2? Maybe I'll wire it in regardless.