where does this plug in go? (Pic)

No the AC comp clutch connector is square. Honestly it looks like the connectors on the 02 sensors. But if you say its by the started solenoid then i dont know. I will check later on today.
 
Looks like the one for the A/C compressor clutch.

I just looked at my a/c plug and it's exactly like that one, so I also say it (is) for the a/c, just look around the a/c and i'm pretty sure you'll find the plug, it could be routed somewhere else though because the other part of the plug has alot of extra wire on mine, took me a minute to find mine also.
 
Do you have your a/c plug that goes in the top of the a/c? if so just follow it down for about 8 to 10 inches and you will find the plug, here is a pic of mine so you know it is for the a/c. 100% Positive it's for your A/C
 
No the AC comp clutch connector is square. Honestly it looks like the connectors on the 02 sensors. But if you say its by the started solenoid then i dont know. I will check later on today.

I guess I should have clarified and said that it looks like the end of the extension harness that goes to the A/C compressor clutch. As dcurtis has verified there is an extension harness that connects the harness coming from the firewall and goes to the A/C compressor.