1999 Ford Mustang GT headlight troubles?

Everytime I drive this car, the headlights will turn on when I turn them on and stay on for a couple of minutes(2 or 3 maybe). After that time has elapsed, the lights will go out. After another minute or so they will come back on etc etc etc this happens until I turn them back out again and the cycle repeats. When I put my parking lights on, they stay on with no intermission. When I put the bright lights on they act the same as the headlights. If I manually hold the turn signal towards me to turn on the brights, they stay on as long as I have it held. Can anyone help me to find out what's wrong?

Added (1). I'm guessing a wiring problem, but I have no clue how to go about tackling the challenge of replacing whatever needs to be replaced xD

You probably have oxidized contacts in the wiring. Using the lights gets the contact warm due to the current flowing and as metal heats and expands, the conductivity reduces. With the lights off, the whole thing cools off to the point contact is re-established.