EEC(computer) should be in the engine bay on a '94, so I wouldn't think you would need any wires on the round connector.
There will be 1 Temp Sender wire and 1 Oil pressure sender wire in there but you can just run new wires from those senders to your dash, maybe a tach wire.
Not sure how you are wiring fuel pump, but you just need the one EEC relay which will power EEC, MAF sensor, fuel injectors, spark module and fuel pump relay(if needed)
I recommend existing fuel pump relay circuit, computer controls it and will cut fuel pump power if engine RPMs drop below 400.
Inertia switch in a dune buggy may be problematic.
So toggle switch or key on closes EEC relay and powers the system, 30amp fuse
The alternator does need 12volts with key on, thats the Battery Light circuit, it will be in that round connector, light green wire, you can either add a Battery Light to dash or just run a "key on" 12v directly to alternator.
An alternator does generate its own voltage, BUT(big but) it can not start to generate voltage unless it HAS voltage to start with, that's what the Battery light circuit does, when alternator starts to generate voltage then battery light bulb has 12volts(14v) on both terminals so goes off.
And it has to be "key on" voltage, if left powered all the time battery will be drained.