Getting a ship to entirely disappear

The best I can do so-far is get a blinking dot on my radar scanner. I'd like a ship that is entirely invisible, so that I don't know it's there at all. Do I have a cloak scanner that I don't know about (I don't think I added one to one of my other outfits, but I can't remember) or is it just impossible for a ship to completely disappear from the radar? Or is it something else?

Yes, it is possible to make it entirely disappear from radar, save for a blip when the ship first appears. All I can say is make sure all the right flags are set on the cloaking device (don't set it to use any fuel or shields) and set all the cloak flags on the ship. But first check that you don't have a cloak scanner

Guy's right about this, settings on the AI ship's chosen cloaking outift will also affect what you see on radar.

There's one in particular that the Nova Bible refers to as 'Visible On Radar' that could be causing your problem.

There's also cloak-behavior flags in the ship resource itself.