It could be either A or K. In fact, the vast majority of GTs in 65 and 66 were A-Codes. K-code cars are pretty rare, even among GTs. Anything other than an A or K is not a GT. One other thing that will disqualify it as a real GT would be a build date of Jan 65 or earlier. The first were built in February. Good luck and let us know what you end up buying!
In addition to Glenn's concise explanation, you might want to set aside between 10-14K for a decent example of a true GT fastback...
I've been looking at fastbacks a lot in the last couple years since I want to replace my race car with a street fastback and have seen unremarkable examples (say a #3-4) in the 8-12K range compared to a regular A coder or C coder, which have been in the 6-10K range out here in California....
If you're looking for a true GT fastback and aren't sure how to distinguish the real thing from a fake, read up and talk to knowledgeable Mustang hobbyists before you plunk down your money...
For an example of what a true K code GT can bring in ragtop form, keep an eye on this auction for a restored example of the breed....
for $35k invested i would expect a little better... i mean come on, where the hell are the front bumper guards? the grill is not supposed to be scraped on a 66 GT and the damn gas cap is crooked. i liked that vacuum advance on what is most assuredly an incorrect distributor. i'd bet reserve will not be met... even at $30k
MCA Gold Card Judge(64.5-65, 66)
'00 GT Conv, triple black
It's good to be observant, especially if your bidding on a high-dollar car like a K-code GT 'vert. I noticed the distro and wire loom covers too. Makes you wonder about everything else said, including the $35K supposedly spent on the resto, that the "stripes down the side" are a feature of the K-code, and "rebuilt to factory specs"
Yes, the K-code 289 Hi-po was available through '67.