I ordered two new fan relay connectors from TPI-Parts because my old ones look like crap with bare wire showing (having fan probs too). How should I install the new connectors? Do I simply splice the new ones in and wrap them with electrical tape, or do they need to be soldered and shrink wrapped?

 

Soldered and heat shrink if you don't ever want to worry about them again. Crimp on butt connectors will work for a year or two if you tape them up good.