I get being in the AZ sun. I was stationed at Yuma Proving Ground (Army) back in 75 - 76. At the time I had a 1969 Mach 1 that I had built to run very quickly. But, it had no A/C. It was bad enough to have lived in SoCal with no A/C before my Army days, but that AZ heat was significantly more punishing than the SoCal heat. I decided then that for any future car without factory A/C I would add it immediately. Our 69 Shelby gT500 has factory A/C that works great, and the 2020 GT500 had A/C as a standard feature.
If you decide to reinstall the factory A/C (I was unaware it had A/C originally, thanks for mentioning it) you will no doubt need to get some partws for the older system. Classic Air has a division that works with older original A/C systems. It may be worth giving them a call to see what they can help you acquire. It is possible you decide to replace the oem system with one of their modern A/C kits. I have called Original Air a few times for parts for the 69 Shelby. They were very helpful, and the original system (with some replacement items from Original Air) is running great.
https://www.originalair.com/
Anyway, even without the A/C it is a nice looking car, one you can be proud to ownyu