If the disk is automatically mounted by the operating system it more than likely has ACLs associated with it; no amount of chown’ing will allow users/groups who aren’t specifically granted permission to do so to access it.
You can check to see if this is the case by running ls -al /run/media/ or ls -al /run/media/garphylet/. Look for a “+” at the end of the permissions; if present, it means that ACLs are in use.
Likely the best solution would be to set up permanent mounts for the disk using the information found in this forum post:
