1990 SW20 N/A Cold start + electrical problem.

I have this problem with my mr2 where the rpms fluctuate when starting cold, sometimes even stalling. Once the car has sat idling for a minute it runs great. This problem has persisted through me doing a minor rebuild on the engine. I believe it may have something to do with the coolant temp sensor, so I ordered a new one and I've ran into something odd. See picture.



The problem is that there is no connector that goes to the black plug below the greenish one (which I believe is the coolant temp sensor). Could the fact that theres no connector going to it be what is causing my 2 to have trouble starting when its cold? And has anyone had a similar problem to me before?

The new coolant temp sensor seemed to fix my cold start problem, as for the black plug, i believe it is for the cold start injector on the turbo model.

The problem is that there is no connector that goes to the black plug below the greenish one (which I believe is the coolant temp sensor). Could the fact that theres no connector going to it be what is causing my 2 to have trouble starting when its cold? And has anyone had a similar problem to me before?
 
The black sender is the cold start injector timer switch and should have a wire going to it on both the NA models as well as the turbos. 
 Look for a wire/plug on the loom somewhere alongside the coolant sender wire. Maybe cut or taped up.