It sounds like your external Library might not be formatted properly. To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. Additionally, the drive can not have had Time Machine on it since it was formatted. There have been so many problems with using incompatible drives that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:
Move your Photos library to save space on your Mac - Apple Support
If this drive is in a an incompatible format, stop running Photos with it immediately! A Photos Library can sit on an incompatible drive, but running it may corrupt the database.
I'm not sure why the Library is grayed out. Even improperly formatted drives can usually give Finder access. Use the app Disk Utility to help analyze the drive. Do you have a backup copy of the Library??
If you're sure your drive is properly formatted in APFS, for example, you might also need to check the permissions for your drive. This is not usually a problem, but it sometimes comes up. Click on the drive icon, and open the Info window with command. Go to the bottom:
Click on the drive icon, and open the Info window with command-i. Go to the bottom:
If “Ignore Ownership” is there, then it should be checked.
