Check this on yours-
The hot wire in the plug to the reverse/upshift switch is always "hot" when the ignition switch is on.
With a test light, find which wire/terminal that one is, on your female plug.
If none are hot - then the problem is up ahead of that toward the cab.
If you have a hot wire, good. The problem will be rearward.
Usually the one directly across and all alone in the plug is the one that gets switched across to - by the reverse switch.
run a 12v jump wire strait to that wire/terminal in the female receptacle plug and you "should" have reverse lights - if All else IS well back to the bulbs.
If no lights working after that test,
start at the rear bulb sockets and work your way back to the front with a test light.
you can use common standard female spade crimp connectors (red size) on the ends as connectors, to connect to the reverse light switch male pins. If you want to eliminate the female receptacle entirely.
Especially if you are just going to use just the 2 for the reverse lights. If you're going after the upshift light too, then you'll need them all hooked up. Radio Shack will have smaller female spades.
You can run new wires out through the old boot and connect to the existing wires, and keep use of the boot.
Might find female spades at RadShk that will fit back into the original receptacle plug. If you want to stay stock.
A cheap-easy option for the reverse lights is a $5-8 dash toggle from a big box autoparts mounted in one of the lower dash bezel blanks.
But its primative eqpt if you have a classy car.
You've already bought the switch(es), might as well try your best to get them functioning with the system, due to their expense.
I've recently priced them.
good luck4u soon