Final answer:
True, an open in one of the parallel branches of a series-parallel brake lamp circuit could cause one or more lamps to not illuminate, as each branch in parallel provides a separate path for current flow.
Step-by-step explanation:
The statement is true. If a series-parallel brake lamp circuit does not illuminate, an open in one of the parallel branches could indeed be the cause. In a parallel circuit, each branch provides an independent path for current to flow. If one branch has an open circuit, the current cannot flow through that branch, but it will continue to flow through the other parallel branches. However, depending on the design of the circuit, this could result in one or more lamps not illuminating. This contrasts with a series circuit, where an open circuit would prevent current from flowing through the entire circuit, causing all lamps to go dark.