Neutral safety switch?

That is one possibility, yes. Other possibilities include internal damage to the transaxle. Did you have any changes in performance of the transaxle prior to this? If not then the switch is most likely culprit.

I have seen a bad starter cause this problem but to be sure this is the issue we can use a test light to monitor the starter trigger wire when in the crank position, if the test light shows a signal the starter is bad.

Here is a guide to help us fix the problem:

https://www.2carpros.com/articles/starter-not-working-repair

Here is the starter location so we can confirm the issue. When you move things around it can cause the starter armature to move slightly and cause the starter to work once again. Check out the images (below). Please upload pictures or videos of the problem so we can see what's going on.