This is more of a PSA question, because they did certify autographs only during phases, despite having the card information on the flip. There are a lot of signed 1963 Topps Pete Rose RC counterfeits (and others) that are listed in the pop where only the auto was authenticated by PSA. PSA has changed their labels over time to clarify whether they are grading the card/auto or just the auto.
With regards to eBay A/G, if you list a signed countefeit 1963 Topps Pete Rose RC (or any other card) on eBay and denote the card is real and the auto is real, I don't know if AG will kick it back or not for being counterfeit. Despite all cards going to PSA to confirm authenticity in the program, the person reviewing it may not know all the nuances of their parent company and pass it through anyways. If the eBay listing only states the Auto is real, it should pass.
If you want more specific recommendations, feel free to send me a PM and I'll look at what you're considering before you make a sale/purchase.
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PWCC: The Fish Stinks From the Head
PSA: Regularly Get Cheated
BGS: Can't detect trimming on modern
SGC: Closed auto authentication business
JSA: Approved same T206 Autos before SGC
Oh, what a difference a year makes.
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