Usually an adjustment will do it. Loosen the two bolts holding the neutral start switch to the side of the transmission and give it a little turn to where it will start in P or N and the reverse lights come on in R. HOWEVER, a common cause of losing alignment is worn shift rod bushings. I'll bet yours are worn or gone. Replacing the bushings is a little tricky but there are lots of tips and shortcuts in them thar archives. Definitely something to check and fix before you touch the neutral start switch.
83 300SD ... $950, see cars forum