Unusual electrical issue, any information about it would be helpful.

The issue I'm having is exactly as follows: Occasionally when I'm driving (usually long distances for hours, but as of this week it is happening more frequently on shorter drives) and I activate either one of my turn signals or press the brake, my electrical system "tweaks out." What I mean by "tweaking out" is that my airbag indicator light flashes on and off, and then the music cuts in and out as if its not getting power to the system, my instrumentation pannel (rpm, gas gage, mph, oil, battery, etc.) All drop down to zero and back up, the accent lighting on all my dashboard devices dims or powers off completely, the clock resets, and worst of all: My doorlocks spontaneously lock and unlock. This is very scary to happen while driving. My solution to this the first time it happened was to pull over to the side of the road and power off my car and then to restart it. After about 5 minutes of driving the problem occured again. I pulled over one more time however this time there was no power whatsoever. No clicking of the starter or any instrumentation lights on inside the car. The door locks were dead and this is when I called AAA. I poppeed the hood of the car and thought it might be a battery problem, I wiggled a cord on the battery terminal and after sitting and waiting for a few minutes the car made a noise that sounded like the electrical system starting up again (a few small parts of the engine moving around and some things powering on). After my car started up again, I drove to big bear with no more issues. We brought the car into the first mechanic who wasn't able to diagnose it but replaced the battery anyway. The problem seemed to have disappeared for a little while but again my electrical system started tweaking out again a few months laterr. Another mechanic who inspected groundings and another failed diagnosis later, we had nothing done. Then later when my headlight went out we brought it into get the bulb fixed, but when we brought it to pep boys the headlight magically decided to stay on for the mechanics there and nothing was replaced (I'm curious as to why only one headlight would go out and then come back on later). After this the car still has the problem recurring and most recently we had all electrical contacts cleaned. Since then this past week my car has been acting up more frequently and Today just now after it was tweaking out while driving I made it back home and pulled into a driveway and powered off my car. This is when the whole electrical system died again (all power was cut and door locks wouldn't work, starter wouldn't click) and then a few seconds later power returned with clock reset and everything else "back to normal." I understand that because this is an impossible situation to reproduce on command that its hard to diagnose. Also, I bought the car used at 40k miles. It was in great condition when I bought it but the previous owner had put on an aftermarket lift kit.