Stan,
I purchased the timer relay you referenced in your drawing from what I can tell. Here is the link timer relay. On the relay it shows the same labeling as what you drew, looking at the relay left side being where the 12V +/- enters, right side top is NC, middle is COM, right side bottom is NO. So when you give 12V power to this relay, it switches the relay and you get continuity between COM and NO (center and bottom) for the set time, then it returns to NC. From your description this would be delay off that is expected correct? If you think there is potentially something wrong with these relays or have a better recommendation let me know, have no problems ordering more.
Here is the actual relay close-up. Overall this is what the entire setup looks like bench.
Dave,
I get modern technology and trains would make this simpler, and I could go in to a dissertation of all the reasons why, but the fact of the matter the first trolley was purchased by my grandfather for me, and the second one was purchased by his wife for my nephew. So these are the two trolleys we will be running 
