It should be an actual on/off button on the calculator thing so you can hear music all the time even when you are not using it.
How about on certain maps there's a small space with something happening in it, there's a camera or 2 or 3 or 500 on it, and when you use the repair tool you can watch whatever's in the space? Or you could use your own .gif files.
Private Sandbag is right, my minigame idea would unbalance the game too much. Maby winning the game shouldn't reward in increased building speed, but as DeadlyDad said, in recovering tool's energy (that would solve the long wall building problem when You need to wait for tool to charge). Game could be limited to walls, alternatively. Or maby the minigame should reward in player experience points?