I got an automatic ‘66 convertible not too long ago. It’s starts and runs good most of the time, but occasionally won’t start. But if you put it in neutral and push it forward or backwards and put it back into park, it then will start. Occasionally, it will start but not shift into gear, or only shifts into drive. Then turn it off and push it again and then start it again and then it will shift into any gear again. Could this all be linked to the neutral safety switch? It has a new starter, battery, fuel injection etc, so I know it’s not that. Just curious if the switch could cause all that or do I have a tranny problem? Thanks in advance.