I'm having the same problem in my 2002 F250. Check out the post below. Its worth a shot.
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I bought an '04 6.0L a few weeks ago, and while I had the dealer fix a few minor problems before signing the papers, they couldn't (or were too lazy to) diagnose what was causing the turn-signal / brake relay under the middle of the dash to randomly click or buzz. I know several on this board have had a similar problem with mixed results having their dealer try to fix the problem, so I figured I'd post what fixed my problem.
The relay that's clicking is mounted to a small harness that can be accessed by removing the lower-center dash panel that surrounds the cup-holders, houses the infamous hook, and has the little cubby hole on the driver side. The relay is inside of a little black box that's just behind and under the cubby hole. After removing the cover and the relay and fiddling around with the five wires that connect to the relay, I was able to trace the interrupting signal to the solid light blue wire. This wire leads through a main wiring harness behind the dash and reappears in a plug on the steering column that goes into the turn signal switch. I won't go into details on how to access the turn signal switch unless someone really wants the detailed process...it's not that hard to figure out if you know how to remove the ignition lock cylinder.
After unplugging, unscrewing, and removing the turn signal switch, I pried open the two halves of the unit. I'm assuming this switch assembly is normally a non-serviceable part, but I figured I had nothing to lose by exploring the guts of it. I have to say this is one helluva complicated switch, and anyone who takes one apart should be VERY careful not to lose parts and pay close attention to how the pieces come apart and go back together...it's very helpful to have a friend help hold pieces during both disassembly and reassembly.
Once the switch was apart, I removed three of the little copper sliding contact pieces, simply cleaned the contact heads by rubbing them lightly with sand-paper, and then re-bent the flat contact "springs" to ensure they would have a tighter contact with the parts they are supposed to connect with. I reassembled the switch with the "repaired" contact pieces and it has completely rid the relay of the intermittent signal which was causing the buzzing / clicking noise. Please note that when reassembling the switch to be extremely careful when closing the two halves back together, as all of the little plastic tabs that move the switches, particularly the one connected to the end of the turn signal lever, MUST be in perfect position as you snap the halves back together, or you will damage the little tabs that move the contact slides (ask me how I know ). Also, as stated before, it's very helpful to have a friend use a small pick to help move the contact slides into position as you close the two halves of the switch back together...I honestly don't think I could reassemble the switch successfully by myself.
Hope this helps a few of you who experience this problem. It took a bit of time to troubleshoot, but it did save me $91 for a replacement switch as well as a trip to the dealership. Let me know if you have any questions!
-Ron-
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