I had the exact same problem of the drive not showing up on the left side of the “Link media” browser (although it was visible and selectable in other functions like “Media Cache Files”). However, I was using an OWC 2 TB drive, with one partition, so it wasn’t an issue of partition size, as has been discussed.
I noticed the original poster was using a new OWC drive, so I thought (hoped!) the issue might just be related to OWC’s formatting application, which I had used for set up.
I reformatted my drive with Mac’s Disk Utility and Premiere’s Link Media browser now recognizes the drive, no problem.
Good luck!