Look closer at the schematic. The bulbs have a hard ground to the body. The trailer harness connectors feed +12 to the bulb sockets. So if the trailer harness was the issue, you wouldn't be getting +12 to the bulb socket. I'd be checking for +12 at the trailer harness.
Pin 1 of T5/T6 is the...
It's a lightbulb. Either you're not getting +12 or there's a bad ground. What were you using for ground when checking the bulb socket? Have you tried a body ground? That would help you determine what you're missing.
The rear side marker lamps are running lights, not turn signals. They come on...