The major thing you don't want to do is pull any levers. The other thing is don't be seen. Most of the clockworks you encounter are inactive unless you cause a fight.
Once you arrive inside the mansion, go through the first door and look up. Break one of the left top windows, a nearby bottle of Pear Soda works well, and Reach up. Follow the narrow path until you reach some big pipes.
In the next room behind some windows are 2 guards. One patrols back and forth through a set of double doors, the other one back and forth in front of a clockwork soldier and a big room. Be careful and don't get spotted. Take your time and peek out to take them out one by one.
Turn right at the clockwork robot. Enter the top of the locked door and sleep dart the guard you can see from there. Take care of the guard that you can see once you have crossed the room and then call the elevator. Take the elevator to the top floor. Make sure you Far Reach to the top of the elevator as it comes to a stop, there are two guards here.
Be careful here again and you won't have much trouble. Take the door at the end of the hall and use Far Reach to get from this area to the next one. Open the hatch and enter the elevator, once again taking it to the top floor. Stay out of the elevator doorway and wait for the clockwork to stop looking for you.
The Clockwork robot is patrolling on the right, so go left in the circular room (using the high machine to get to a long shelf) and look for the perfect moment to take out Jindosh before he notices you. Shadow Walk works well to get you over there for a Stun Mine zap. You can also hit him with a sleep arrow or crossbow bolt. If you didn't kill him, you have to go down one floor to put him in the chair. Select Anatomy and Optics.
Be careful of the clockwork down there. It might be the same one from above, if you didn't do anything to it.