Recently, I have found my IPOD TOUCH, 4th Generation from 2010.

Wiped it clean and it restored to iOS 6.1 - the most recent OS it will handle. Still works great for music and photos. No issues there.

I used to be able to read ePub books, but that app seems to have been lost and no longer available from The App Store.

Does anyone know where I can find an out-of-date version of iBooks or some other app that can read ePub books on this iPod?

Found this, so see if it works for you: "Go to the App Store on your [iPod]. Click on your past "purchases", everything you ever installed [iBooks?] will appear here. Install from there and it will ask you if you want the old version."

Afterthought: does the very old iPod even have App Store access??

Hehe. That WAS the first thing I tried (i.e. no longer available at the App Store).

There are any number of EPUB readers available in the App Store,,There are any number of EPUB readers available in the App Store, I have no idea if any of them will work. I suspect it’s the 32 versus 64 bit issue that is going to rule the anything it currently in the App Store out.

Yes . . . BUT, I am looking specifically for OLD apps which the App Store no longer supports.

Before I replied above I did a fairly extensive search (partly because I too have a very old iPod). While there are a lot of readers, all of the ones I saw required iOS 10 or later. That may indeed relate to the 32 versus 64 bit issue.