1996ford mustang v-6 5speed if headlight switch pull out is bad will it cause battery to discharge?

The most likely cause would be the relay. An auto electrician with a pro grade scan tool computer can instruct the relay to switch on and off to test them. It could be the switch, but test before replacing. The AE tech can do that too as he has access to the wiring colours.

https://www.google.com/search?q=2005+Mustang+GT+high+beams+cause+headlights+to+go+completely+off

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Do a parasitic draw test to find the cause ! Don't guess ! If someone on here said yes would you change it ? An suppose it didn't fix it ?
The BEST Way TO Perform Parasitic Draw Test

Usually caused by failed alternator. Remove the alternator and have it tested at your local parts store.

Usually the high /low dimmer switch on the column goes bad or a headlight relay, headlight switch supplies power to the dimmer switch.

If you have a light control module then that is probably failing. However if the dome light is activated by small switches in the door pillars it is possible that the contact points may be rusty or have a bad earth.

try disconect baterry for % mins while battery disconnected ,switch headlights on to discharge computer box capacitors .......so it loses fault memory........reconnect switch ignition on and wait 30 sec before starting .........see if light re appears afterwards .good luck

The headlamp switch or the multi function switch(turn signal,wiper switch) is causing your problem. Find out what switch is cheaper and replace it. I've seen the headlamp switch go bad more than the multi switch.

your switch is bad. had same problem on my 1970 mustang with the headlights flickering unless I pulled on the switch. I replaced the switch and they work fine now.

Probably either a bad ground (broken wire, rust) or a bad headlight switch. The brake light circuit goes from the stop switch (Located up above the brake pedal) through the headlight switch, through the light bulbs to ground. The tail light circuit goes through the headlight switch, through the bulbs and to ground. The only things that are in common are the headlight switch (Is this the switch you replaced?) and ground.
Not much, but hope this helps.
Have a super day!
Ron

This is copied from a manual on CD I have, Hope it is of help.


Instrument Cluster Finish Panel

Removal and Installation
1. Disconnect battery ground cable (14301).

2. Remove headlamp knob from shaft by extending to headlamp ON position. Press clip in slot of knob shaft by inserting a small tool and pulling back; at the same time pull and remove knob.

3. Remove two screws retaining instrument panel finish panel (044D70) above instrument cluster (10849).

4. Pull instrument panel finish panel to unsnap one retaining clip above LH register.

5. Pull instrument panel finish panel on both sides to unsnap two retaining clips.

6. Pull instrument panel finish panel by sides of steering column to unsnap two retaining clips.

7. Pull instrument panel finish panel to unsnap three retaining clips on RH side vertical/horizontal edge and remove instrument panel finish panel.

8. To install, reverse Removal procedure.