More (kinda) secrets have been discovered as The Rat Pack achievement in World of Warcraft Legion's renewed Karazhan was completed a few hours ago! Since this doesn't seem like something that players could have missed for this long, it's very likely it was simply patched in this reset. Nonetheless, redditor Fenderz was on one of the first runs to get the achievement and shared what's needed:
Directly after curator and before medivh there is 5 rats you can click on the ground that give you rat mounts that are consumable and lost on exit of karazahn. You will lose the rats if you die while mounted!
If you accidentally kill the rats you can exit and reset the instance as long as medivh is alive.
2 right out of the curator portal, 1 on the ledge right after jumping down,1 on the right with the pathing inquistor on the ledge, and 1 at the end of medivhs twisted hallway
It seems there are issues with the rats themselves though, as you will lose them if you use shapeshift, certain leap skills (like the Demon Hunter's) and they can even bug out and replace a Hunter's pet instead of becoming mounts, so beware.