Sorry about the techno jargin but ohms are easy, it's how you measure resistance in a wire, call it traffic report on the interstate -parking lot (resistance) or smooth sailing (no resistance).
Leave the connector disconnected from the switch. The switch is what I want to figure out if it's working or is creating a short to ground that is blowing the fuse. Chances are it's the switch but given the $72 price tag at Ecklers I would want to confirm it before buying one.
An easier way to test without a meter is to make a jumper wire and bypass the switch, trick the lights into thinking your in reverse when your not. If you have a piece of wire a foot in lenth or a little less would be fine. If you don't have it go to a local parts store, walmart, ace hardware, home depot, etc. and pick up one of the soldier less connector kits with a crimping tool if you don't already have one. These kits have different type and size connectors with at least one fitting for this test. They are normally a hanging item with red, blue and yellow connectors in a plastic see thru package.
I don't have a 4 speed switch in front of me so I can't tell if the wiring harness end that connects to the switch has a female or male end, I'm gonna guess female so you would want to use the flat spade looking crimp ends either blue or red depending on the gage of wire your using, if the harness end is male then use female connectors. Put a connector on each end of your wire then put the connectors in the wiring harness end. The wire will be a loop now.
All you've done is connect the 12v power wire in the harness to the wire next to it simulating what the back up switch does. If the lights come on and you don't blow a fuse then you know the backup switch is the source of the blown fuses. If the fuse blows then atleast you've narrowed it down to the wiring to the rear, the sockets or bulbs.
Let me know how it turns out and I'll be glad to help out in any other way I can. Good Luck
Now I'm off to take the boat out on that big lake they call Atlantic
and head up to Peanut Island with my wife.
I carry a blackberry so I get email notifications if you run into a problem I'm not totally out of pocket.