Take the frame to a painter, they'll remove the original finish (usually by hand with abrasives) and start from scratch.
Second hand carbon is second hand carbon... you can't always know what the previous owner did to it/with it.
Thanks, subsequent googling has come up with exactly same advice both on painting and reliability or not of second hand carbon.
@JoePablo started
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Take the frame to a painter, they'll remove the original finish (usually by hand with abrasives) and start from scratch.
Second hand carbon is second hand carbon... you can't always know what the previous owner did to it/with it.