The reverse light switch is a common failure item - I know people that have replaced their switches more than once. When I bought my '00 RT/10 used, the switch had already failed (at less than 13k miles). I recall think the part cost around $30 (not sure now on the cost) and takes less than an hour to replace, depending on the tools you have available.
The switch just screws into the outside of the tranmission, so replacement is very straightforward - only wrinkle is getting to it. Some people say they can replace it without removing the plate under the transmission, but I had to remove the plate to get to it. I seem to recall I got good use out of my ratcheting box-end wrenches to get the switch in and out. An air wrench is very helpful for speedy removal and replacement of the plate, due to the number of bolts.