1st pic (connector being held near drivers side headlight) looks like temp sender. Does your temp gauge work? Sender is on the block under the coil on mine.
Ive just re-organised the wires at the front of mine. Cut out all the bullet connectors, soldered them properly and hid the wires inside some tubing I got off ebay. Hey presto all work perfect.
Quite why they put a load of exposed bullet connectors behind the grill is beyond me.
The temp gauge is working...
Sounds like a good idea about soldering the bullet connectors, not sure if im brave enough to do it myself though, whenever i do anything on the mini something else breaks lol