Now consider Derek's circuit. One clip is on the bulb's glass, not on the holder's screw.

Electricity goes into the bulb only through the holder's two metal screws.

The holder's two screws touch the bulb's two metal parts.

So the loop has a gap at that screw, and the bulb stays dark.

A clip on the glass leaves a gap at the screw, so the bulb stays dark.

Now consider Dexter's circuit. Both clips are on the same end of the battery.

Nothing touches the other end, so the loop has a gap there, and the bulb stays dark.

Both clips on one end leave the other end bare, so the bulb stays dark.

Now consider a wire that is cut through in the middle.

The loop has a gap at the cut, so the bulb stays dark.

A cut wire leaves a gap, so the bulb stays dark.