I think I'm close, but wondering if I still need to ignition module?
Not sure what you mean by module, as your '73 would never have come with one, so does not have factory wiring for one.
But with EFI, whether using a distributor or coil pack (all you said is it's modified) all ignition duties are completely controlled by the computer and are accommodated in the engine harness. No chassis harness wires needed at that level.
I am running a 2000, 5.0 Explorer motor, EFI guy customized the harness and computer.
Sounds more like that means you'll be using the DIS and coil pack, rather than a distributor? Or was that what the modification was for?
Either way, non need for those wires (yet) to control anything on the engine side, other than perhaps as a keyed power source for the computer. But then that would depend on how you have it wired, and where.
Also, are the wires under the dash that plugged into the old motor needed?
As already mentioned, if you're going to be retaining the original gauges, then the water temp and oil pressure gauge sending wires go through there.
Remember, the sending units for the computer/engine and the sending units for the gauges are completely different and incompatible with each other. You can't use one set of sensors for both here, like they would in most newer cars.
If not needed, is one of them hot with ignition?
Yes, but with a catch.
The red connector should have a Red w/green wire. That's your old coil wire but is a resistor wire which won't provide 12v under load or after it heats up some. It's designed to reduce the voltage to keep the old ignition happy.
If you're using it to energize a relay, or something that does not need the full 12v or need much current, it should still work. Or you could bypass the resistor part in the middle and simply jumper that directly to the same color wire at the ignition switch.
If there is another wire there, something like Gray with a blue stripe maybe? Or Blue with a black stripe? Then it's 12v with the key too.
You can test these easily with a voltmeter though. Since we don't know the condition of the old wires, you're better off physically testing each one anyway.
The square-4 plug is your old neutral safety and backup light connector.
You may or may not need it, depending on what else you've done.
Paul