As I have fully embraced iCloud, I had not synched any iOS device through iTunes in a long time, but intrigued by your question I tried with my iPhone (iOS 10) and iTunes 12 (MacOS 12) and had similar results to yours except I was unable to induce the iPhone to mount as a drive at all. So in spite of my normal inclinations I went directly to the last resort, iTunes Help and found...
Note: If you use OS X v10.9.3 or later, you can sync only contacts and calendars. Other types of info are updated on your computers and iOS devices via iCloud. For more information, see iCloud Help at icloud.com. (Emphasis mine)
From there I went to iCloud.com ➭ Help and after some searching found…
iTunes, apps, and books content everywhere
On your iOS device, see the Music, App Store, and iBooks sections of the user guide for iPhone, iPad, or iPod touch. For a device that doesn’t use the latest iOS version, get the user guide for iPhone, iPad, or iPod touch from the Apple Support manuals website.
From there I searched out a copy of the manual
for your 4th Generation iPod Touch (iOS 6.1) and from that the best I can come up with is you must delete each item manually on the iPod Touch.
Other than that, the best I can offer is to revert to OS X 10.9 on your Mac, which I cannot recommend.