The right bulb

The right bulb follows a different rule.

It should light for 0 + 1 and 1 + 0, but stay dark for 0 + 0 and 1 + 1.

Its rule is: exactly one input is on.

No single gate from earlier follows that rule. OR comes close, but it also says yes when both inputs are on.

The circuit needs to exclude that last case. That takes more than one gate.