but this topic is the only one I've found that actually gives a working solution to the not syncing issue.
As an FYI for future questions, you can just create a new topic. That's how this forum is designed to operate, when asking a question. But it's good to read existing topics... 🙂
All of the music I currently have on my iPod is in my library now, so is it only syncing purchased songs?
If all of your songs are in your iTunes library on your computer, you can try a few things including a Restore. And NO, purchased songs are treated the same as other songs for iPod syncing, if you have authorized your computer for the Apple ID used to purchase. If the computer is not authorized for the Apple ID used for purchase, old songs purchased from the iTunes Store may not sync due to DRM (copy protection), and you'll get an error message. More recent iTunes Store song purchases no longer use technical DRM. And there should not be a case where ONLY purchased songs sync using automatic syncing, if you are setting it to sync the entire music library.
You recommended checking off the Sync Music option under the Music tab when looking at the iPod.
That's not just a "recommendation." That is the one and only way to set up automatic syncing. And with iTunes 12, it is no longer accessed on the "Music tab." In iTunes 12, select the iPod in iTunes. You initially see the iPod's Summary settings screen. In the sidebar (along left side of window), click Music under Settings. To the right, you see the iPod's Music settings screen (what was previously the "tab"), where the Sync Music checkbox and other music sync settings are located. Assuming you are using the latest iTunes version, is that where you are looking?
If you check the box for Sync Music, select the option to sync Entire music library, and Apply the change, you should get your entire music library on the iPod (assuming your iPod has the capacity to hold your entire music library). NOTE: Be sure to look at the checkbox on the iPod's Summary settings screen for Sync only checked items. If that box is checked, and you have songs that are unchecked in your music library, only the checked songs will sync.
Pick one of the songs that does not currently sync. Make sure you can play it in iTunes. Do this with the iPod NOT connected, in case iTunes is somehow accessing the song's file from the iPod. If you can play it in iTunes, iTunes knows were the song's file is located on your computer's drive. If iTunes has lost track of the locations of some song files, then those songs will not play in iTunes, and iTunes will not sync them to the iPod.
Otherwise, since you have ALL of your songs in your iTunes library, you may want to do a Restore on the iPod using iTunes.
Restoring iPod to factory settings - Apple Support
This erases the iPod, reinstalls its software, and sets it to default setting. You can then sync the empty iPod from your iTunes library, with the Sync Music / Entire music library setup. All songs should sync.