In the basement, I have an idea. See those two light lamps hanging from the ceiling? There may be something hidden or taped within those cone shaped light fixtures. Reach into them and prod around for anything unusual.
Also, wave the key card on them for good measure. 
Mr. Stick looks at both lamps, and, indeed, notices strange shadow going from left lamp. He examines it more closely...
Yes! There is some item hidden in the lamp! Mr. Stick takes it.
Good eye! Now mr. Stick has a KEY.
He also moves keycard in front of lamps, with no effects.
Mr. Stick stands to think about it.
Even if this place is super weird, full with hidden mechanisms, still - there should be logic in all of this. And secret cardreader, invicible for human's eye, falls from this general logic picture. Something must give you a clear hint that there's secret cardreader in some object, or some other secret item or mechanism. So, before you got that hint, there's no need to use blindly some item on another.
By the way, cardreader could be hidden inside the lamp, for example, but at the same time, he could be visible for human's eye. Mr. Stick wants to say that you didn't ask him to inspect lamps more closely before. Even if there wasn't key or won't be cardreader inside, there still could be something. Another item, writing, etc. Mr. Stick should be more observant to details and be more inspective.
