If the shift interrupter is being engaged when shifting out of gear into neutral only but not when shifting into gear then something is causing resistance on the cable/linkage movement.
Typically when a cable goes bad you stall shifting into gear and especially when shifting into reverse.
If this only occurs when shifting out of gear into neutral then something is causing this resistance.
As BT doc suggests, disconnect the short cable with someone at prop, shift it yourself manually while the prop person is rotating the prop. Counter clock wise for forward and clock wise for neutral.
You should be able to push the cable end in and pull it out with minimum resistance. If you have to pull hard or push hard then the cable will be suspect.
When pulling or pushing to go back to neutral have the prop person HOLD the prop from moving and as you try to get back into neutral it should become very hard to get there as the clutch dogs will not want to separate (most times as the system is not under normal load). This is what happens normally and this resistance is what activates the switch and cuts out the ignition for a split second.
Also does the V notch plastic part move freely. WHat motor do you have? is this a 4 cylinder with the shift interrupt on top of the valve cover?
I have come across 4 cyl motors as I described where the V notch hold down screw was over tightened causing too much resistance on the V notch movement.