1993 Ford Ranger Headlights won't stay on

I have a 1993 Ford Ranger XLT and for a while now I have had a problem with the headlights sometimes cutting off a few seconds after I start up the motor, usually when I'm accelerating (this could just be a coincidence, as I usually accelerate a few seconds after starting up). Sometimes they come on and are just fine, sometimes they don't come on at all, and sometimes they come on and then cut off after a few seconds. A while back they had a similar problem when they would cut out after having the brights on or having something charging in the 12 volt plug/cigarette lighter. The parking lights always stay on and work just fine. I have changed the bulbs out, so they are not the problem. Could it be a loose connection? Could there be a short somewhere? If so for either, where could it be and how do I fix it? Any help or info would be greatly appreciated.