Summary: I have multiple services that have the exact same set of cached tiles. There is no documented way to have these services point to the same tile cache folders so I don't have to have multiple copies of the same tile cache sets.
Proposed solution: Create a symbolic folder link from each of the "other" services that points to the "master" tile cache folder location. I have created a ticket w/ ESRI, but the result of that is: "Yes, I think that would work, but that is just an opinion. Perhaps you should check with the ESRI community to see if anyone else has ideas or feedback."
Detail: I have one ArcGIS Server site that is running on the Azure cloud using three Ubuntu Linux servers and the data stored on an Azure hosted PostGRESQL server. Server 1 and 2 have ArcGIS Server 10.9.1 installed and are accessing a shared drive that is hosted on Server3 where the shared site folders are stored. This is where the cache directory is stored.