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

Right. Good. Helps me too.
A couple comments
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.

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.

And drawing note: On a 1970 the J1 wire feeding the ignition switch will be 12 gage red. I drew it as a black feed because one year in the early or mid 1960s the shop manual shows it black.