Rex placed many adv in the later Ford Owner and Dealer magazines from late '25 to the end of the T production in Aug 1927.
While most famous for the 'rumble seat' conversions for open roadsters, including other makes like Chev, Dodge, etc, the Ford runabout was a favorite with Rex modification.
Don't think the Rex Co ever 'built' and sold completed cars, only sold the body thru distributors to auto dealers or shops who specialized in modifications to autos at the time, it was popular to do 'conversions' back then.
The bodies were made for open cars and a closed sport coupe, note the fine print detail on the roadster body, it was made of fabric covering, not typical metal over wood frame construction, most likely to keep down cost and weight of the body.