This question came up about 6 months ago, IIRC, and there wasn't much in the way of a concrete answer. Translation - a few dealerships may offer rental units, but it is not a universal thing. I believe that MCD RV on Cape Cod, Mass, does so, but that isn't much help to you.
The big problem is that in order to rent a unit, your tow vehicle must be equipped to tow it - meaning a weight-distributing hitch, electrical connector, and brake controller. If you don't already own a trailer, this is an unlikely situation, of course, but if you do have a properly-equipped tow vehicle, so much the better.
The alternative is to have the dealership deliver a TM to the campground of your choice and set it up for you - but then you don't get the towing experience you seek.
When you rented the TT, what was your tow vehicle?
I would suggest that you simply call the dealers who are within reasonable range of you, and describe what you are looking for. You can find a dealer listing at the TM website,
www.trailmanor.com.
Bill