Good thinking! I suspect you have a small short circuit, likely in the very wires we're discussing. I had a DOZEN or so little breaks, nicks and such in my 50 yr old vinyl insulation on the stuff from the starter relay and the headlight+battery wire in that loop. SNIP! SNIP!, and ONE nice NEW wire thru the firewall took care of those issues. If you've got time, get a good digital voltmeter and go around the dash and underhood checking various voltages. Start from your starter relay. Try disconnecting the battery, then do a continuity check. Check resistance to ground on those wires which give you a "ring" on continuity. HEY, did you check the windshield wiper hookup?! THAT's a likely sort of sneaky short we're hunting.
Do your relay setup for the EFI now, just to optimize available potential to it. You will still have a problem, but this should bypass it to a healthy extent. I had to hunt down my wiring problems over about 6 months, and I only now, about 13 months of happy ownership later, can say I'm confident in my wiring harness. I still need to setup my headlights on a relay too, but for the present my ELECTRICAL issues amount to simply upgrading and adding NEW elements, finally! You'll be happier when you get there too.