Cannot use service url as input to some geoprocessing tools (Make Image Server Layer, Make WCS Layer, Download Rasters, and Add Rasters to Mosaic Dataset with Image Service type) if the service does not reside in the root folder of ArcGIS server
For use in geoprocessing tools, drag-drop the image service from ArcGIS Server connection to geoprocessing tools instead of using a string. There is no workaround in python scripting.