Disconnect connector at back up light switch. With ignition on, use your multimeter or test light to make sure you have battery voltage on brown wire of connector. If no, you have a wiring,problem or problem with connector C230. Will have brown wire there also @ cavity H of connector.
Connector C230 is located under right side of dash behind kick panel. If you have power to brown wire at back up switch connector, use a jumper to connect to side of connector which goes to back up light. That would be terminal that has the light green wire. This will test wiring, connector C400 and splice S405. If back up lights come on, all is well between back up switch and lights.
If lights don't come on when jumped, you have problem with light green wires, Connector C400, or Splice S405. C400 is bolted to hatch release bracket at back of car. It has 3 wires & 2 ring terminals. S405 is located in rear body harness, approx 5 inches back from grommet p400, which is back up wire grommet.
If all is good with wiring, connectors, splices, this leaves the back up light switch as being possibly defective. Remove switch from trans. I assume that you will lose some fluid. So have a clean pan to catch fluid. I've never looked at a t56 back up sw, so I will assume side of switch that goes into trans has a button that gets pushed or pulled by trans shift forks.
For this test use your multimeter set to ohms. When switch is in normal position, there will be no continuity between leads where connector hooks up. When switch is pushed or pulled, depending on what you have, you should get continuity between the 2 leads of switch. If no continuity, your new switch is bad. If switch has continuity, & all other tests proved wiring & other things are good, then you can look to trans for problem.
You can get 94 service manual at following link. My Files
Back up light wiring diagram starts on page 8A-112-0
Also t-56 service manual at shbox.com