No that is not normal. There has to be enough slack to allow for sharp turns of the outfit and often the cable may even touch the ground and requires a little strap to hold it up. From the end of the towhitch another 18-24 inches should be available to you. Sounds like someone has chopped it for some strange reason.
You do not state if you have one, or two cables for the 12N and 12S sockets, or is it a 13 pin set up?