Unfortunately I don't have Skyrim installed any more, otherwise I'd take a look myself. But if you go here: http://www.creationkit.com/Perkyou'll see a screenshot of the dialogue box for a perk. When you go to edit one of the Entry Points in that screen, under Perk Entries, the dialogue that opens should have condition tabs that apply to the items I mentioned (player, target, etc.). The "Run On" value is a numerical index for those tabs - again, as far as I understand. I could be wrong.
Edit: Just to clarify, the "Run On" field I'm referring to is actually called "PRKC - Run On (Tab Index)" in xEdit. There is also a field just called "Run On" which is different.