Note that I don't actually subscribe to any/all of these statements, just trying to think through potential reasons and arguments.
How and why did the car get to the train station?:
1) Robert drove it there himself, to take a train. He took a train instead of his car because he felt his car was noticeable/traceable/identifiable if found with him. He did not leave the car in Brooklyn and take the subway either because he wanted to intentionally misdirect regarding his disappearance, or he was taking the train to eastern LI. Robert getting on the train in this scenario is an intentional and permanent disappearance. If he was doing something temporary i.e. "a surprise for the wife", he wouldn't have gone without his wallet - he had to have cash or a ticket already. A darker variant of this scenario has him disappearing, only to find a place to take his own life where he could not be easily seen or found.
Thoughts: This sounds fairly plausible to me.
2) Robert drove it there himself, to meet someone. "I'll meet you at the ticket house or near it, by the red Pontiac, at Deer Park." Not an unreasonable place to meet someone for some purpose. Since his family was not aware, it's extremely likely that there was something "wrong" about this meeting. Sex, drugs, blackmail, etc. In this scenario, again due to the missing wallet, Robert may have either then intentionally disappeared after the meeting, on the train by himself or with the other person, or got in another car with the other person. A darker variant of this scenario is that the person or persons he met with took him away unwillingly and he was killed, and his body hidden.
Thoughts: This also sounds fairly plausible to me. If it was a premeditated disappearance, it seems very possible he had an accomplice or at least a plan involving someone else, either at Deer Park or at some other location he went to via the train, as with option 1 above. With both, it's notable that if he was in Huntington at 1:45pm, he was on his way home earlier than usual (usually arrived home around 3pm according to wife.) This fits a premeditated scenario in which he wanted to get a "head start" without rousing too much suspicion (as he would have if he had skipped out on work - he called his wife from there at 9am.)
3) Robert drove it there himself, during some "episode"/mental state of confusion. Then, he disappeared and ended up somewhere not easily found, either via an accident or random foul play in his vulnerable state.
Thoughts: I find this doubtful. I don't think he could have or would have driven and parked there in a confused mental state. And if he did, he would likely have been found or seen by someone, he could have asked someone for help. If he had gotten on the train in this state, the conductor would have become aware of the problem. The wife has not replied yet to the question about his alleged headaches or any possible existing condition.
4) Someone stole the car, and drove it to the station before ditching it there, the perp either getting in another car or hopping on the train. The phone in this scenario may have been taken by the perp, and the phone either died on its own or was intentionally disabled, or the foul play event happened after the last cell phone ping, between Huntington and Deer Park. Robert must have come to harm in this scenario, and the perp is either someone he knew or had dealings with (allowing the crime to take place out of view) or a random stranger.
Thoughts: I found this doubtful. I believe his wife saw where the cell phone pinged roughly in Huntington and it made sense to her as being on his way home. The odds of someone carjacking him or similar earlier, and then coincidentally driving the same way he goes home, and going to a train station near his house, seem slim. So any foul play would have had to have happened after the cell phone ping at 1:45pm near Huntington. But I don't see what really could have happened to a 6'1'' 200 lb man in broad daylight in that region of Suffolk County if he was just going home on his usual major thoroughfares that would result in him being carjacked, robbed, and killed, without anyone seeing anything or the body being discovered.