Here’s more:
I had removed iTunes Helper from the “log-in” items on my primary account (and forgotten all about it). So today I look again and it’s back!
So I created a new folder within /Applications/iTunes.app/Contents/Resources (“Removed_iTunesHelper”

, put iTunes Helper in there and logged out. It’s back again, in my log-in items, persistent little bugger! So I zipped it up, renamed the zip and deleted the original. So it can’t come back. But… you’ll never guess, iTunes
turned itself into a Start Up item all by itself.
That’s where I am right now, I removed it from the login items and logged out again but I think it’s still starting up after sleep, I’m not quite sure yet.
Once when I was poking around in iTunes prefs (trying to solve this problem) I found under Advanced, this:
So I clicked it, fully expecting the button to turn into “Unset”. Nope, same button.
So I searched around in the iTunes prefs file to try and find a pref to turn this off, can’t find it. Does anyone have a clue on how to undo that “Set”?