I installed a power valve for my black tank this summer as the original cable hand operated valve had failed. I still use the manual system for my 2 grey tanks. So far all is good.
To answer one of your questions, yes the manual lever is on the electric valve which is under the belly fabric.
I had only 2 wires to connect to 12 vdc power, a grey negative and a black positive. I connected these to an accessory fuse panel that I had installed in the battery compartment when I was installing my battery switch.
Note that ground wires on RVs and related equipment are coloured white (sometimes light grey).
Positive wires on RVs are coloured black. On a car or truck, negative is black and positive is red.
Internally in the wiring harness, the ground divides to supply both the motor and the switch on light. Same for the 12vdc positive supply.
I would use an automotive 12 volt test light for trouble shooting. Attach the black wire of the test light to a good ground by using it's clip.Touch the pointed probe to any wire you want to test for power and the test light will illuminate. If the motor is healthy and has power, you will be able to hear it run also.
Don't destroy the belly fabric until you make a diagnosis with the test light that the motor is toast.
