I have a stock s13 and every time I connect the battery the fuel pump primes and the small red dash lights turn on, I can put windows up and down. it basically goes into accessory mode. If I turn the car on it will run and drive fine but it doesn't shutoff even if I take the key out. I checked the relays and there all good as well as fuses. I heard somewhere it could be the oil pressure switch/sensor or possibly alternator back feeding but I am not sure. Really looking to get some help on this please let me know what you think!