It is difficult to say what colour are the wires. If one is pink and the other pink/blue (move the insulation a bit to see if there is a second colour on the wire) - then it is the thermo-time switch plug. Be careful as you may be getting "+" on the pink/blue wire (if it is still connected) when you crank the engine.
Thermo-time switch is part of starting aid for the engine - it provides ground in certain conditions to a relay that activates the Cold Start Valve that injects aditional fuel to the manifold to make start easier. The Thermo Time switch is in the engine block, its upper part, drivers side, near 5th and 6th cylinder. Apparently you have it wired in a different way or you have troubles starting the engine. Lots of info on this on the forum (Thermo Time Switch or TTS).
If the colours are different - then I do not know, we would have to know the colours to check on the other fellow Mambers suggestions.
I would also review the wiring on the contact plate on the gear box - it looks different from what I remember from my gear box, but maybe it is just a different type of solution (emission control?). The contact plate should have a cover. There is no wire on the hydraulic switch (under the plastic nut). Do you have issues of engine stalling when you put in Reverse gear? Do you have idle speed adjusted by a solenoid on the intake manifold? This switch, in some engines, activates the solenoid that increases idle (Constant Speed Solenoid or CSS) when reverse gear is selected. Again - in your car there may be a different system to do it (emission control?, CSS sometimes works for air condition only).
Normally on the kick-down switch you have a 2-pole plug and a retaining spring.
I see also some lose wire hanging there with eye connector - maybe it is better not to leave it hanging...