You need to start PublishingTools geoprocessing service from ArcGIS Server Manager page.
Refer the following help page about how to do it:
http://resources.arcgis.com/en/help/main/10.1/index.html#//0154000002st000000
So you receive the error "Bad Syntax" when trying to cache your service? What happens if you use the Manage Map Server Cache Tiles tool under Server Tools > Caching? Also, can you change the logging level for the server to verbose under Logs > Settings > Log Level? It'd be beneficial to get a better error message other than bad syntax.
I'm still getting this message even after restarting and confirming that my PublishingTools service is running. Any other ideas?