Started tasks may be in the ICHRIN03 started procedures table in RACF. You haven't mentioned anything about using the started procedures table yet, but you certainly should be investigating it at your site.
If you have no documentation, your best bet -- if you are allowed to -- would be to dump the RACF data base into a sequential file and look at the 0404 and 0400 record types for data set protection. The data set names being protected would give you some idea what naming standards are in use at the site. If you need to look at the FACILITY classes, the 0505 and 0500 records would have that data.