Before I go on to anything, I'm not responsible if your harness goes bad or you fry your ecu or your car blows up or whatever, but here is what you should at least TRY.
1. Locate the pink/black wire coming from the EGI relay2. Cut it3. Get an ECU pinout (
http://www.kouki.co.uk/referen...nouts ) and locate the Fuel Pump Relay, pin #18 on your ECU plug. It will be a yellow/black wire4. Connect the pink/black and yellow/black wires. DO NOT solder them until you have tested it and have made sure that this does/doesn't work for you.
This is what I did after I completed my swap and it has worked fine ever since. It seems to be something with notch tops getting swapped into s13's that causes this. I am not saying this will definitely fix your problem because you very well may have something else going on, but like I said, you should at least try it to see if it works. Hope this helps Good luck with the rest of your swap!