What do I need to do on the first floor?

Hint 1 of 7:

You may talk to the chefs.

Hint 2 of 7:

Or, better, you may examine the room.

Hint 3 of 7:

Have you noticed the rear side of the clock?

Hint 4 of 7:

Isn't that the clock which does not work and makes the tattooist wait?

Hint 5 of 7:

Try to repair it!

Hint 6 of 7:

Do you have a cog with you?

Hint 7 of 7:

You may have found it in the castle.