The mystery part number is (wait for it) C5ZB-17B587-B which is the windshield wiper switch to motor harness for a single speed wiper.
Now for basic troubleshooting. If you have a 12V trouble light, the type that looks like a pen with a bulb on the top, a sharp point at the other and a 24 to 36 inch wire from the bulb end that has an alligator clip at the other end, you can see if you have power to the tail lights. If you don't have one, get one, it makes electrical life easy.
For all this you need to have the battery hooked up, the three prong connector to the switch disconnected and maybe someone looking at the tail lights (it helps with two people).
1. Find the hot pin in the connector - clip the alligator clip to something metal close by, then use the sharp point on each of the three contacts, pins or sockets, of the connector that goes to the main harness. When the bulb lights up, that's the hot contact. Do all three contacts.
2. Clip the alligator clip to that hot contact (pin or socket and MAKE SURE THAT THE CLIP DOES NOT TOUCH METAL), and then place the sharp point in one of the other contacts. The fog lights will come on with one of those contacts, the remaining one is the circuit that goes to the tail lights.
Some warnings: don't keep the test lamp in the circuit too long; the fog and or tail lights will not be as bright as normal; you may burn out the test lamp bulb. If the fog and tail lamps both come on, the problem may be in the switch.
Jim