If yours is the aluminum case 2 speed tran., there is a hole in the switch that you slip a drill bit in when in neutral. Loosen the adjustment then slip the drill bit in to adjust/align the switch. Also, all the throttle linkage needs to be adjusted right first.
out of the book:
NEUTRAL SAFETY SWITCH ADJUSTMENT: Check
starter circuit in all selector lever positions. The
circuit must be open in all positions except "N" (Neutral)
& "P" (Park). To adjust, loosen switch-to-steering
column attaching screws, then shift selector lever to
"N". Rotate switch as far as it will go in either direction,
then insert a .060" pin through switch housing at
gauge pin hole. NOTE - This hole will be located at
end of switch housing or on the upper side of housing
depending upon type of switch used. Hold pressure
against gauge pin and rotate switch in the free rotation
direction until pin engages hole in plate. With gauge pin
through housing and into plate, tighten attaching screws
and remove gauge pin. Check starter circuit in all
selector lever positions. Starter must operate with
selector lever in "N" (Neutral) or "P" (Park).
1960 COMET, FALCON & EDSEL