Trying to help my Dad get his car going and has a battery that keeps getting drained. There is a light under the dash that stays on all the time and most annoying is the door buzzer goes off all the time when you open the door even with no key in ignition. The buzzer will go off if the switch is depressed. I relize that chances are there might be more then this going on.
What I'm looking for is what is the best way to track down any gremlins lurking within the elctrical. Do you need to chase every wire and check? Get a test light and check every wire? Hoping someone has some input that may shed some light on this. Thanks for any info.

If you can swap out the battery or have the equipment to really test it would be great start. I have found the battery to be an issue many times and I had overlooked it because it was new or it worked fine before. that's not the case however. Start simple, the last thing you want to do if find out it's something easy after hours of hunting around. I would suggest pulling some of the fuses for the interior lights and buzzers like you stated.

as far as the bulb, unless u can find the correct location for it, just take bulb out (until the dash gets rebuilt/repaired) and that issue is fixed. the buzzer is another issue that could be a bad ground, bad horn relay (if d buzzer is housed on d horn relay like my 68), or bag ignition switch (which i doubt). i would simply disconnect the wire to the door(or doors) buzzer until issue it gets fixed. this is just temp so that batty wont drain. it could also be a bad or shorted buzzer pin switch in the door jam. that buzzer is anoying -even when it does work correctly. if the other door buzer door switch works ok, i would remove that one and try it on the one giving u probs, or u can remove bad buzzer, hook up an aligator clip wire to body of buzzer and the other end to good ground, then connect it to the 12volt source. if still same issue then its ur buzzer switch. i would try a good buzzer switch first though. if its same issue then ur looking at a short in horn relay (which are not expensive) or ignition switch.

finally, a test light will help u determine that d buzzer switch is getting good ground (grounded to chasis) and good 12v source (plug that goes into buzzer), confirm this first before moving on ...thx
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What vehicle?
Chevelle, before 1972, the key minder buzzer is in the horn relay and the pink/black wire turns on the buzzer by becoming a ground when the key is on AND the driver's door is open.

Sounds like maybe the little switch under the steering wheel that the key operates is shorting out to ground.
Try unplugging the pink/black wire from the horn relay.

The light under the dash may be related if the problem is in the door jam switch.
Try unplugging the wire at the jam switch.

Thanks for the suggestions guys. It's a 71. That's a good idea about hooking up a good switch possibly the other one and unhooking the wires from the horn relay. I'll be sure to give the ideas a shot. Hopefully it will be that easy. We probably won't do a good restoration on it for several years. Just looking to get it somewhat reliable to cruise on weekends and to shows. Thanks guys.