It appears to be impossible to add any behavior which bestows non-zero detection without the yellow "detector" label showing up in the unit's information. If a value of -1 or > 0 is placed in the "detection range" property, the "detector" label will show up.
I'm trying to find the best workaround to solve my problem. Specifically, I'm wanting to have a unit able to detect hallucinations but not cloaked/burrowed units without the yellow "detector" label showing up. Does anyone have any thoughts on the best solution for:
1) Simple two team gameplay (simple detection of enemy unit allowed)
2) FFA gameplay (detection needs to be enforced for each player)
None.

I do stuff and thingies... Try widening and reducing the number of small nooks and crannies to correct the problem.
You could add the detector behavior to an item unit and add the behavior on the item. That may work.
But how does that help you to make a detector that only detects hallucinations?
You could add behaviors to hallucinations that they are detected that tint the colossus.
But I don't think that this would be only visible by the player.
Maybe attach a model to the unit with the behavior...
uhm... maybe I have more ideas tomorrow...
You could add the detector behavior to an item unit and add the behavior on the item. That may work.
I believe that items bestow behaviors to the units holding them. It's pretty much the same as just giving the unit itself the behavior in the end.
But how does that help you to make a detector that only detects hallucinations?
That part's trivial. It can be done by modifying the detection filters.
None.