Fixed this problem myself 2 mos. ago
(just posted this reply to a guy w/ similar problems over in the '97-'03 F150 Forum)
I recently had the same problems - both turn signals sort of going crazy... blinking out of rhythm, then stopping altogether. Very puzzling. And the dash blinking matched the lights. No bad bulbs/lamps. They all worked.
Suggested problem areas were: the turn signal switch/master switch (inside the column), a loose connector - also inside the column, and the turn signal relay/flasher.
What I found was that the turn signal relay (also called "flasher") was bad. It's a part that costs $12 or so and can be replaced yourself. It's located under the dash, is about the size of a 1 inch cube, and has prongs (think electrical plug). A knowledgeable guy at O'Reilly's was very helpful in getting me the right one, and that made it easier to find what I was looking for under the dash. When I found it, it just unplugged (the factory unit had a piece of tape around it - removed that) and I plugged the new one in.
Again, the part was incredibly simple to replace. In my '02 F150, however, I did have to exercise extreme patience and acrobatics to (a) remove a ton of various little screws to get the bottom dash panel (by your knees) off so that I could see better to find the flasher. You might or might not have to do that. Should be located below and slightly to the right of steering column as you're facing the dash. (not when you're laying upside down on the floorboard, half in and half out of the truck... from that angle it's to the left of the steering column...)
Important note - disconnect the negative battery cable before doing any of this...