With iTunes 12, the iPod appears in the horizontal bar that goes across the window (near the top), as a "device button." With "normal" settings, when the iPod is connected AND iTunes is running, iTunes only mounts the iPod's disk while syncing. When syncing is completed, iTunes unmounts the iPod's disk; that is why the iPod no longer appears in Finder. iTunes does this so that the user can physically disconnect the iPod without "ejecting" it in iTunes first. If you want the iPod to continuously appear in Finder while connected (with iTunes running), on the iPod's Summary settings screen (in iTunes), set it to Enable disk use (and Apply). With that setting ON, iTunes does not unmount the iPod's disk when syncing completes; the iPod remains visible in Finder. The user now must Eject the iPod in iTunes before disconnecting it. NOTE: When the Manually manage music [and videos] setting is used (instead of automatic syncing), Enable disk use is already ON.
But the iPod needs to appear in iTunes before you can Enable disk use on its Summary settings screen (accessed by clicking the iPod's device button on the horizontal bar in iTunes). You don't see the iPod's device button in iTunes when you connect it?
If not, this forum category is for the iPod shuffle. When you connect it with iTunes already running, what does the shuffle light do immediately after connecting? If this is NOT a shuffle, what does the iPod's screen say when you connect it? In either case, does the box at the top of the iTunes window say anything related to the iPod (such as "iPod sync is complete") after connecting the iPod?
It may help to know the specific iPod model (including "generation").
I'd simply like to access the files on the iPod just like I may be able to access the files on, say, a SD card, a flash drive, etc.
With Enable disk use turned ON, you can access the iPod's disk like it was an SD card. However, you cannot manage its media that way. To add songs to the iPod, you use iTunes to sync the iTunes library to the iPod (either manually or automatically). So, if you are new to Mac (and did not previously use iTunes on your PC), you need to add your songs to your Mac's iTunes library first, and then use iTunes to load the songs you want on the iPod.