Fuel pump problems.
So i recently picked up a 1986 300zx turbo manual. Its got a couple minor mods done like wheels, exhaust, coilovers, and an air intake. However, my biggest problem is my fuel pump. Something happened electronic wise with the car in the past that affect the fuel pump system. To start out, what the previous owner has done is they have taken one of the plugs that powers the fuel pump while the car is running and basically bypasses the relay and is taking power straight from the plug that powers the wipers and has it grounded in the trunk. So now I have a super ghetto wiring job that isn't the safest, and also am without wipers. I know the wipers work, but the plug is just being used to power my fuel pump. The car runs fine with the way it is wired currently but it is running rich at idle as it isnt connected to the computer and is just getting a constant voltage. Now when I try plugging in the pump to the plugs that it is supposed to be connected to, the car will crank and start for a couple seconds then die after it is out of fuel from being primed. I've checked the relays and fuses that relate to fuel delivery but they seem to be working/fine, but the fuel pump just wont kick in when the car is actually started. Im not sure if there is an inertia switch somewhere that has gone bad and isn't allowing the pump to run, if so, where would i find it? Is there anything else that anyone would recommend I check? I'm trying to check the simple things first to narrow the problem down as much as possible. Also the guy that sold it to me told me that the owner before him had the battery on backwards, Im not sure how someone does this but I guess he was just very oblivious. Im not exactly sure what all this could've damaged. So far everything electric that I know works is the g-meter and compass gauge, all the seat adjustments, and all the lights. Gauge cluster is out, and so is the radio. Any input or advice helps! Thanks.