I want to turn the sneak eye off via the ini settings (a mod does this with SKSE so I know it "can" be done) and I thought I would just browse the ini settings. But now I cannot find the post that had the full dump of the Skyrim.ini.

I found http://pastebin.com/hJBtab6g PasteBin link. It might contain what you need. If you're willing to use a mod, then at least Immersive Hud or Skyrim Compass Tuner should be able to hide the stealth indicator.