The NSS is just in the crank circuit.
When you say the sol clicks, are you referring to the sol on the starter ??
If the starter sol is clicking ,then you have to have to see a light working at the test terminal near the booster
Anythin after that test point goes to the starter . it is the FEED line to the starter sol.. the NSS circuit feeds that point , so if No light there ,the problem is before that test point..ie-NSS, ignition, ATA ,etc

Have you tried both N and P ???????
The adjustment could also be off from when the sw was installed .. this is checked by holding the key to start while moving the shifter on both sides of the N gate...you can not do this in P cuz P is at the END of the gate [ no room to go past it to allow for mis-adjustment]