After checking, I found there is continuity between the top two terminals of the switch when it is pressed down. To complete the installation, move the ground wire from the lower right terminal to the upper right, then remove the upper left connector from its terminal, and substitute the yellow wire in its place. Zip tie everthing in place for neatness:
And here's what the end result looks like; just as stock, and an installation that can be removed later if necessary with no cut wires, etc.:
Next will be to box in the bottom of the cooler with a piece of scrap aluminum or plastic as Chuck did, but I guess that can wait until next summer.
Hope this helps someone!
ianc