NOTE: This walkthrough was written for the first beta of CotC. The mission may have changed since.
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If you frob mushroom 1 it will change, as will all adjoining mushrooms - 2,5 and 6 Mushroom 6 will change: 1,2,3,5,6,7,9,10,11
If a mushroom is on, it goes off. If it is off it goes on. You want to turn them all on.
The solution to this puzzle was provided earlier - in the scroll that was in the wagon. Remember the odd page numbers? A3, C2, A1, C4
Imagine the block of lights as a grid. From the top down, the rows are: A,B,C From left to right, the columns are 1,2,3,4
The page numbers correspond to this grid. To light all lights push A3 (top line, third from left, C2 (bottom line, second from left), A1 and C4. All lights should be lit and the last door open.
Put the Flute on the stand within.