This one appears to be a '65. (At least, it has '65 knock off wheels.) Very few vehicles from 1965 had air conditioning at all. Besides, why have air conditioning in a convertible. BTW, I owned a '64 convertible, very similar to this one. The thought of buying air conditioning never even crossed my mind.
I used to work for a guy who had an early 60’s vette convertible with factory air. IIRC, it was one of 200 made that year. I think it was a 1967. Her lost it when upon trying to sell the car he had purchased legally, it was discoverd to have been stolen a couple years before he bought it.