Hi David
Welcome to the Forum and finally your first post.
I only remember one rail line on the Hamilton side of the Beach, I have seen pictures with two lines on the Burlington side but there was only one on the swing bridge.
However, looking at the early 1900's picture of the house at 771 Beach Blvd (The Alps) there looks to be a rail line in front of the house, this was most likely the radial line.