Yes . That is the first sign of a failing NSS.
The P and N contacts in the NSS are the same set , they are just activated in a different position. So, failure in P usually leads to future failure in both P and N .. which means Tow Truck. N only will get you started for a while, but it is a matter of time for complete failure/no start.

The reason I also mention shifter bushing is b/c if the linkage is sloppy from a worn bushing , the NSS lever will not fully engage in P as the shift panel does not allow full movement as the cover acts as a stop for full travel, whereas in N , you have room to giggle it on either side of the N position.
Another reason for NSS failure [ aside from normal wear] is they are susceptical to water and dirt due to their low location on the side of the transmission.
Not an expensive part and an average DIYer can do this job...
The sw. does have elongated mounting holes for adjustment and this sw also incorporates the contacts for the back-up lamp circuit...