I know this quest well, as I repeat it every conquest week for more Skeleton keys on My current Main THF and my retired THF.
Read the information here:
http://wiki.ffxiclopedia.org/Bait_and_Switch
Also, another side note:
http://wiki.ffxiclopedia.org is your friend. I find most, if not the greater majority of my information on the wiki first.
Edit: Oh and to clear up your confusion:
There are 3 switches.
Large Switch, Medium Switch, Small Switch.
You need to deactivate these switches in a certain order to successfully deactivate the trap and obtain your reward. See a random switch order example below.
1. L
2. M
3. S
4. S
5. S
6. M
7. L
8. M
As you can see, the small switch must be deactivated in the third, fourth and fifth spot.
These are done one after another.