The images below might help.

 

If it's an early 66 (or 65) with an emergency flasher that is hard-wired into the wires then the emergency wires will plug into the turn signal plug and then the wiring harness plug (what you took a picture of) will plug into that. Kind of a jumper. If you have an emergency flasher that unplugs from the wires then that's not the case; the harness plugs directly into the turn signal wires coming out of the steering column.


The Wiring Diagram book is really helpful for these connections and it's only a few dollars.

 

It would really help if you told us what year car this is? Hint hint

 

?‍♂ sorry overlooked that. It's a 67.

 

Ok that helps. The white connector I believe you are referring to appears to be the connection to the sub harness on the back of the instrument cluster. The turn signal connector is similar 10 pin connector. You’ll have to look at the connectors or the wire colors to confirm which is which.

 

That plug looks like it has 12 connectors. That and it's position makes it look like it's the one for the back of the instrument cluster.

Based on the wiring diagrams I think the one for the steering column will only have 10 connectors. That's likely the one on the other side.

 

Thanks for your help everyone! My new cluster with full size tach is coming on Monday and I'll put my turn signal switch in as well. I'll post results here.