Q: iPod classic won't sync into iTunes 12.4.1.6

Hey there amenalum, 

Welcome to the Apple Support Communities! 

Here's a great resource for getting your content back into place. Having those tunes in multiple places, gives us all the freedom to jam out all day long. This will work for items that were originally purchased from iTunes: 

Redownload or transfer your iTunes Store purchases from an iPhone, iPad, or iPod to a computer

Other original media, outside of iTunes purchases, would need to be re-imported to the computer. Once your content is back in place, here are the steps for creating an iTunes music library back up: 

Manage and back up your iTunes media library

Cheers, friend.