The NSS is on the driver side of the transmission where the linkage connects.
If I understand you correctly, you select Park, the transmission is IN park, but your reverse lights are on. You also have to put the shifter into N to crank the starter.
If that is the case, then you simply loosen the two 10 mm bolts that hold the NSS to the shifter shaft and adjust the NSS position (the mount holes are elongated for this) so that the reverse lights are on in R only, and the truck should crank the starter in P and N. If it still won't crank in P, you may need to replace that switch.
If that is NOT your problem and the transmission really IS in R when P is selected, that means the cable is stretched or its mount clamp got loose and the sheath slipped. I have no experience with any of that. although my FIL's 2000 Grand Marquis had a similar problem. We found a Torx head bolt on the driver's floor. I put it back into the column and it fixed that. A good visual inspection of your cable should find something like that.
Welcome to The Ranger Station!