If the starter engages when you wiggle the shift lever, likely the shift rod bushings are shot. There's a bushing at either end of the rod between the bottom of the shift lever and the transmission. When the bushings go, there's slop in the shift lever. It should be tight, as in no fore-aft slop.

I forget where the NSS bypass connector is in a 126 but it must be somewhere ahead of the battery. You jump a couple of open connectors to engage the starter. It's one way to determine if the problem is the NSS or starter.

Sixto
87 300D