Have you looked at
What is image service caching?—Documentation | ArcGIS Enterprise on updating caches. It looks like what you may want to use is the Compute Dirty Area—Help | ArcGIS Desktop to help determine what needs to be updated.
This tool constructs a polygon that defines regions containing one or more mosaic dataset items that have been modified since a specified point in time.
This allows tools and applications that depend on the mosaic dataset for the construction of derived products, such as cache, to perform partial updates since the last time the derived products were synchronized with the mosaic dataset.
and Map cache updates—Documentation | ArcGIS Enterprise for updaing
I have not had to update my mosaic/Image Server service caches yet, since they are still fairly new. But it looks like there are many other tools that might come in handy in the Mosaic Toolset (see left hand column TOC when on the Compute Dirty Area help)
