I know dozens of collectors who would gladly pay thousands of dollars for an authentically signed Neil Armstrong baseball. These guys are on eBay all day long. The selling price of this piece tells you all you need to know about what knowledgeable collectors think about its authenticity.
Neil Armstrong signed baseballs are exceedingly uncommon. He hated signing them. If you were lucky enough to get him to sign a baseball, he typically applied a very rushed slapdash signature on the side panel.
Jfried504 has listed another item from Coach's Corner. This Jim Morrison "signed" LP was previously listed by eBay seller jjcollector123, and was removed by eBay earlier today.
How about this from eBay seller Jfried504/JJcollector123:
Bought from a private collection from a long time collector of music items and records.Said he received it from his father in the 1980s.I’m not a collector of music memorabilia so I’m not an expert and I don’t know much about jim Morrison. The albums was shown to a local collector who collects albums and he said it’s the greatest example of his signature that he has seen and he compared it to other examples and he said it matched completely (though he is not an authenticator of any kind).