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To solve the puzzle:  Line yourself with up the horizontal arrows with the vertical arrows until they intersect on the bottom room.  When they match up kind of like this >^>. Head to the 2nd part of the room with all the fake arrows.  Line yourself up with the arrows pointing up from the previous room that intersect.  On the bottom room they show 4 arrows starting from the bottom where they intersect.  With that visual clue in mind, move exactly four steps north from bottom of the 2nd room where room #1 points up.  Hitting your action button on this specific tile reveals a hidden switch which opens the way to the next floor.

That was certainly a can't see the forest for the trees moment for me. Thanks for the reply. I can move on now. :)