Welcome to the Team Mike!
Harrison, or Frigidaire compressor with cast iron brackets with GM casting numbers on them, a fiberglass case on the fire wall with a huge hole in the fire wall for air flow of outside air (aftermarket bores two small holes in the fire wall just for the hoses to pass through, no outside air ducting), and vents in the dash (not a knee knocker hung under the dash) along with tinted window glass indicate a factory A/C car.
Factory air was rare in '62 but they were offered as an option. Most were dealer installed A/C units with York compressors and stamped steel flat brackets (except for the welded platform the compressor sat upon).
Trim tag should have group two letter code "E" if it had factory air conditioning.