Juan I work with people on Ebay to identify parts and help them with their classic Ford cars. I also own 3 old Ford Galaxies 60, 62 & 64 2 dr hardtops. I have been playing with Fords for years since I was 15, I'm now 53 and still own these cars and attend many shows.
There really is a 1964 1/2 Mustang. It truly is a rare car especially a convertible. Unless this car is already butchered or the engine was swapped out years ago and someone repainted it resale Red then I really do agree with D W in the first response. Save it if it is all complete with original parts, it can be worth a lot of money if restored back to original.
The difference between 64 1/2 to a 1965 Mustang
is minimal but to a collector HUGE. The 64 1/2 has a generator where the 65 has an alternator. There is a difference in the radiator core support which is removed in 65 to 66. Engine options change in 65. The 260 V8 is only available in 1963 and 1964. It was originally used in Falcon and Fairlanes and 289 V8 was for larger cars but also optional in the Falcon, Fairlane and then the Mustang. In 1965 the 260 is dropped as an option, so 260 V8 are pretty rare and are the same except for bore and stroke of the 289. You can do a lot of upgrades to the 260 and 289 as they are. The 289 is NOT a 5.0 that is a 302. The 289 is used from 1963 to early 1968 models then the 302 takes over. Same basic motor as the 289 but bigger bore and stroke, also the 351 Windsor comes into play which is also the same block as the 289, 302 and 351 Windsor. The 302 is the 5.0 motor still used today. So 302 and 5.0 are the same basic motor. I have friends that have swapped the 5.0 straight into 64 Fairlanes, 65 Mustangs and even Galaxies.
There is an internal difference with the 64 Ford engines from 65 so they are pretty rare engines and you need to know what exact year you have if you rebuild. You also need to find out if it is a 260 or 289.
My suggestion to you is to buy books or read up on the Mustang and learn the difference, join a club and go to car shows and talk to people. This will give you a good idea on how you want to build your car. More than anything what ever you decide make sure you save those original parts and make it easy to put it back to original. It will be worth a lot more and do it right the first time.
The Mustang was introduced to the public April 17th 1964 at the Worlds Fair. Check the VIN to find out when yours was built, could be close to being number 1 then it is worth tons more.