Lets look at Illuminated

The Illuminated advantage is an exotic one that lets its owner be aware and part of a secret conspiracy. It was part of GURPS Cabal, GURPS IOU, GURPS Voodoo and GURPS InNomine which are all essentially supernatural conspiracies. It was ported into Fourth Edition pretty much as is.
If, however had it been built for Fourth from scratch what would it look like?
I have tried building it but its a bit clunky.
Start with Detect (Conspiracy), is it Rare [5], Occasional [10] or Common [20]?
That your noticed is a limitation, though the reaction bonus would be an enhancement. Possibly a wash. Making it cost the same as Illuminated [15] would require +50% on Occasional or -25% on Common.

The Case for Detect

In a conspiracy campaign Common is probably about right, the PCs would be more involved in it, plus the secret masters would have tentacles everywhere.

• Discern others on Sight without error, sounds like use of Reliable but could be accounted for with the +10 for in plain sight bonus.
• Others spotting you would be an Active or noisy limitation.
• The +3 Reaction Roll is perhaps a Reputation bundled into it. Treats as Rep +3, small class of people [5].
• Floating certain skills to the higher of them or IQ is probably a feature.
• So Detect (Conspiracy) [10] + Reputation 3 (Illuminated, small group) [5].

That makes for Active Sense, -50% on a Detect (Occasional) to account for others with this advantage being able to not only spot you but sense your influence in affairs.

Why Bother?

In making this a Detect various modifiers can be applied such as Vague, Precise, Targeting, Analyzing, etc.

Also I feel Detect should have some kind of Active limitation, so that works too.