Original paint on a '69 Vette would most likely be a single stage laquer. Before attempting to do any paint correcting, look carefully for any signs of checking. Checking will look like a hardboiled egg that was rolled around a countertop so as to crack it very finely. If it has any signs of this stop now and cut your losses. Next, I'll ask, are you actually removing swirls or light to medium marring (
see this post for the diffrence)? If they are swirls, they will need to be polished out most likely using a rotary with a series of steps. It's best to start with a light to medium polish or glaze using a foam pad and check your results. I like to use 3M machine glaze for Dark colored cars or Auto Magic BC-2 on paint like this (this is just me though, use what works for you) If they are not being worked out, move up to a more abrasive product (something like 3M Finesse-it II or Mark V Uno) then back to the lighter polish. Follow this with a sealer, glaze, or wax. If it is not swirls, but marring you need to remove a DA with a light to medium polish will usually remove them -- so will many sealers as well as glazes. Without seeing the paints condition though, it is almost imposible to direct a treatment for your ailment. Back to the paint -- easy way to tell if it's a clearcoat or a singlestage is to rub a liitle polish in an inconspicous area using a white towel, if it takes on the color of the paint, chances are good it's a single stage paint.
... An unhappy one tells many friends 
!!!
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