Hello and thank you for using just answer. First the taillamp failure circuit does not monitor reverse lights on your car, that is a seperate issue related to brake/parking lamps in the rear, be sure all other bulbs are working also. Reverse light issue-here is the repair manual sheet to verify source of condition, if you have a manual trans the back up light switch is a simple switch on the transmission case, if automatic you use a neutral start switch to power the lamps, see below:
Download 4 -see page 1 of this download
If automatic transmission equipped the neutral start switch is somewhat common but as always I do recommend testing/verify problem before spending time and $$ on a repair to be sure you are not throwing parts at a car that are unneeded.