Hey Dan , it's Greg. Want to say sorry again for the bad parting on words previously and welcome you back into the game with a fully operational vehicle. A man and his jeep , it's a beautiful thing.
ok , it probably is the back up switch on the transmission . I guess you already found it on the passenger side. Follow the wiring harness up to the firewall where you can find the connector under the hood . The factory service manual 1992 ( don't have a 1999 but ought to be similar) shows the plug to be located on left side fender shield. Color black. Will be a two wire plug. Disconnect it and use a test light to look for power from the dark blue w/ white stripe wire . You want to read voltage with the ignition on from the harness side of the plug . With plug disconnected , you won't find power on the switch side . If the test light shows power , jump the two terminals together to verify if the back up lights go on. If you had back up lights before with the old trans , I'm sure your wiring circuit should be fine. But this test is good to verify.
To confirm if switch is bad , use an OHM meter and probe the two terminals in the plug on the back up switch side of harness. Ignition can be off but e-brake on and select reverse and verify if ohm meter reads continuity. If meter reads no change between reverse and neutral and good connection is made with meter to plug terminals , the switch is bad. Changing it will just involve unthreading it from the case with the appropriate wrench. Seal the threads with loctite to prevent oil leaks. Let us know how it goes and post back if further assistance is needed. My best , greg
P.S. - forgot to mention , there probably is no specific fuse for back up as the back up lights share power with several other systems and may be marked in the fuse panel as sharing with other circuits . If all your fuses ( regular , mini & MAXI ) are good , and all lights works ( brake , turn , marker , etc. ) you should be good and most likely the switch. One thing to check ;
since the trans was installed after removal for clutch replacement and a replacement trans swapped in , BE SURE the wiring harness is plugged in at firewall and if there is a separate disconnect at the trans and that there is no damage to any wiring in the back up light circuit.
