Don't let these naysayers get to you. There weren't a LOT of Mustangs with trailer hitches but I have seen my share of them. Many of them tended to bolt the hitch, at least partly, to the rear bumper which has about as much strength as a dish towel.
I think some of them would weld a steel beam on the back side of the bumper to give it more strength.
Unibody isn't a problem for tow vehicles; there are a lot of such vehicles made. I own one myself; a W124 Mercedes. These guys might be amazed at the kinds of cars you see in Europe with trailer hitches on them. The problem with an older Mustang is finding something at the rear of the car that can accept a hitch. The biggest thing back there is the gas tank and I wouldn't recommend bolting into it with your hitch.
Direct from the mouth of the people who built the horse I have attached a clip from the 1965 Mustang sales brochure. It says that even with the 6-cylinder engine you can tow up to 2,000 lbs with your pony. Of course, they recommended that you buy about every option they sold in order to do that towing. But remember, these guys were in the SALES business.
They reference the '1965 Ford Car & Truck Recreational Brochure'. I don't have a copy of that but there are many of them for sale on eBay, etc. I have no idea what else it might tell you. It could be interesting or could be meaningless. The 1977 version of that manual is online and has a page for the Mustang II which might be interesting - see attached.