I disagree. There is no reason at all to show lights if what you are really testing is sensitivity to radio signals.
There's no parlor tricks here. The lights are the placebo in a placebo-controlled study.
If you want to determine if a medicine is really the cause of the effect on patient's health - positive or negative - then you use a placebo to rule out the possibility that swallowing a huge pill or getting an injection itself is causing some psychological effect. You have the real medicine (lights+signal), fake medicine (lights + no signal), control group (no lights + no signal), and sometimes an alternative treatment (no lights + signal).
There is a known (or at least claimed) correlation between WiFi signals and reported illness. The test is designed to isolate the effects of perceivable stimulus (lights on the device) with the supposed cause of the illness (the invisible WiFi signals). Intuitively we all "know" that WiFi signals do not cause any physiological effects. But something is apparently effecting these people, and the test is aimed at figuring out what that something is.