Dookr Locks gone Haywire!

I own a 2002 Ford Ex Eddie B V8. It has 82,000 miles. I have an after market remote start and recently added a built in GPS/ Stereo system. A few weeks after the GPS was installed, (could be coincidence) the auto door locks just started click on and off, as if someone was pressing the switch. This would happen when the car was started, then stop after about a minute or two. After about a week or so, the door locks, along with the auto lamps stopped working altogether. After checking fuses, I tried disconnecting the battery, and everything went to normal for a few weeks before the locks and autolamps started click on and off intermittently for a couple of minutes after starting. Disconnecting the battery would temporarily solve the issue, but now it at a point where if the battery is disconnected, the locks will work. Once the car is turned off, they will not work again- along with the auto lamps.