If I'm reading between the lines correctly, it's not the aircraft that was the sensitive item, but the translucent canvas for the shelter.
It was meant to send a signal to our adversaries: "We can't cover up anything"
I'll refer you to several earlier posts in this thread instead of explaining again why this isn't a translucent or transparent cover over the metal ribbing of the ClearSpan structure in the images. Over the past months, I've asked a few of my suppliers - who are leaders in the industry - if they have ever heard of a transparent ClearSpan-type aircraft shelter. The consensus is that no such thing exists.
However, although the aircraft itself may not itself be some sort of new,exotic airframe (as many seem to want it to be), It's role and presence at Groom Lake certainly are sensitive. For example, if one of Draken International's F4s or L-139s were being used to test a new sensor or electronic warfare system, a savvy hostile analyst might be able to figure out what was being done based on what aircraft was being used. The aircraft may have been carrying systems or modifications that need to be concealed. Most of what happens at all test ranges would seem extremely mundane to most enthusiasts, and the skies over Groom Lake aren't constantly filled with exotic aircraft (especially in this age of advanced computational modeling).
I could be wrong, but I still suspect that this is N543J, which has an airworthiness certificate valid until August 2022. It's currently owned by a holding company that may be leasing it back to a contractor, or it may be a Small Business contractor dealing directly with DOD. If so, it's ADS-B transponder certainly wouldn't be active during flight ops within NTTR.