what you will find is the upper dashboard paints were low sheen to prevent glare and the lower including the glove box had more sheen but were still not a gloss finish. I think if you check out restoration parts for as many 60's American cars as you can you may find suitable spray can of black. A word of caution with this area to paint; be aware that over the years the parts you want to paint may have accumulated some wax or worse some silicon e.g.. from putting Amour-All on the dash pad. This is a formula for disaster known as "fish eyes". The fix is really simple. Use a good wax and grease remover from a paint shop and then clean everything a couple of times using dish soap and hot water. I would remove the glove box door and paint it first to see if you encounter fish eyes as it's easy to sand the door down and repaint it as many times as you have to. Unlike enamel, lacquer overspray is not much of a problem because it dries so quickly while enamel overspray can get on everything requiring a lot more masking off of surrounding areas. I like using lacquer because you can mix it to spray nicely through a PreVal sprayer which I generally get at Ace Hardware. In addition, should you find that you are getting fish eyes, you can buy some fish eye eliminator at an auto paint store. Also an auto paint supply house should be able to mix the correct GM formula and give you the sheen you want. This won't be cheap but you'll like the finished product.
I hope this helps.
Doug