There's this place in Indiana that rents them. Not sure if that's the same place you mentioned. It says its in Markle IN.
https://www.i69trailercenter.com/rentalsI've seen their rental trailers during move in at MCACN.
I started digging around a bit in 2021 trying to find if any places in the Chicago area rented enclosed trailers and didn't find anything. There may be some available around here but at least searching online I wasn't finding anything. I gave up on taking a car to the show I'd registered it for then, and was finally able to get a trailer deal from a local guys estate completed after some setbacks in time to trailer the car to the show this year. Seems sort of expensive and inefficient to own, license, maintain and pay storage on a trailer I'm only going to use 2-3 times a year, but you gotta do what you gotta do I guess!
I think it's pretty hit or miss, there are some places that rent them but its not very common at all like rental open car trailers are.
