...........X2.........UNLESS............the battery is nearly dead. What does the battery read? If battery is "up" then first place I'd check is the fuse box for corrosion, loose clip, even a defective fuse.
Your circuit path for the parking/ tail lamps is (assuming majority of vehicle is operating OK)
Fuse panel "hot" buss from ammeter---------through fuse---------to B2 of headlight switch connector------through switch----back out connector--------to the left kickpanel connector--------to rear harness--------to rear sockets
Each point in the above path is a possible poor connection
