Can't access iPod's HD from computer

Hi.

I'm trying to fix a problem with a 40GB 4th Gen Clickwheel iPod.  (It's actually the rebranded HP version.)

Almost everything seems to work fine except that I can't get the iPod to connect with iTunes or even show up as an external drive when plugged into a computer.  I've tried it with multiple Macs, multiple versions of macOS (Catalina and High Sierra), and also with a Dell laptop running Windows 10 and iTunes 12.10.10.2.  Every time I try to connect the iPod, its HD goes into an audible clicking loop that repeats about every five seconds.

I tried moving the iPod's HD into two other known-to-be-working 4th Gen Clickwheel iPods and still get the exact same behavior, so that seems to indicate that the problem is with the hard drive and not the dock connector or other hardware component in the iPod.

So why does it play music 100% correctly, and respond correctly in all ways when operating independently of a computer, but not when it's plugged into a computer?

There is one other oddity:  the iPod's About window specifies 3041 songs, 37.1 GB capacity, and 37.0 GB available.  Clearly those 3041 songs must use more than .1 GB of disk space, and there are also some podcasts on the HD.

If I could just find a way to get access to the contents of the HD, I would copy off the music files and restore them into a new iTunes Library and then install a new drive into the iPod and reload the music.  Does anyone have any suggestions for how I might get at the contents of the iPod's current HD?

I already know how to make the hidden files visible if I can just get the HD to mount on a computer. And, no, there is no backup or original iTunes Library from which to restore. I can continue to use the iPod as-is until the HD eventually dies, but I’d like to be able to add more music to it and, more importantly, secure the current music files before the HD fails completely.

Thanks in advance for whatever insights you might be able to offer.