Why won't my running light on my 1993 f250 shut off unless I disconnect the battery?

must be a bad wire if you put a new battery and alternator in it. Are you sure the battery and alternator are good. One way to test the alternator is to run the engine and disconnect the battery [one post] while the car is running. If the car keeps running, the alternator is good. If engine cuts out and shuts off, alternator is bad

sounds like a bad crank position sensor

you may have a bad ground, or the ignition switch needs to be replaced.

No read the fix below.

Engine stalling issue at low speeds

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve. Buy a can of throttle valve cleaner from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

light switch is bad.,,,,car should not run down the street,with battery disconnected,but it shounld idle,

Try this. Lock and unlock the tail gate with the key and see if it will start. The battery must be hooked uo when this procedure is followed. Whenever the battery is disconnected, the security circuit shuts the ignition down.
When you hook up any battery, make certain that you connect the positive battery cable first and negatvie (ground) second.

The day time running light module on the back side of the front drivers fender likely needs to be replaced to fix your problem.Unplug it and the lights will work normally from the headlight switch but the day time running lights won,t work and also the high beam indicator light in the dash won,t come on when you switch to high beam but all the lights will work properly.You should replace the drl module as soon as you can but unplugging it will at least keep you from having to remove a battery cable.

Go to Autozone or O'reilly auto parts and have a free charging system test run, sounds like the alternator is failing.

check to see if the ground wire from the battery to the engine is tight if the cable is loose it will cause the injectors to flood the egine

When u power up the vehicle ABS does a self test(light stays on a few seconds then cuts off) and if it see's a problem will shut off and illuminate the ABS lamp. It will also do a second test on iself when you reach a speed of around 12-15 mph,it will run the pump for a few seconds to check pressure and look at the speed sensors,if it see a problem here it will again shut down and illuminate the ABS light.
Now if the red brake lamp is on then it will shut down because it thinks you have a hydraulic concern and will not try and run ABS if this is the case.
If red brake lamp is on most likely if you have good brakes it is a problem with the float sensor in the master cylinder reservior,maybe its bad or just stuck,or just low on fluid.