Time-based puzzle box

PaulS

What would that action be? If the clock is dead, it no longer knows the time. The only appropriate action that I can think of is to open the box.

Exactly. If I ask for the time, and none is available (for whatever reason), open the box.

Driving a servo, no. Powering the servo, yes. Don't do that.

I think I understand what you mean - the Arduino will switch the servo, but not provide power to it. Correct? I assume there are examples of this online.