If you built that turntable yourself, you know it has two copper wipers against two metal rings separated by a bit of styrene. They are constant, so when the turntable turns 180 degrees, its rails will be out of phase from the opposite side when metal tires try to bridge across the gaps. You must either wire in a reverser IN SERIES, or wire in a DPDT IN SERIES. Either way, they get wired into the turntable's feed wires, the ones rising to the bridge rails.
Most turntables us a split ring design below the pit. Those rings are always fed by the same wires, so they don't change. However, their are wipers running against them that feed the bridge rails. As the bridge passes over the split, the wipers change over to the rings that have the 'other' polarity or phase (depending on DC or DCC, respectively). That effects the reversal you need, so you need no reversers or switches. Not in this 90er's case, unless they have redesigned it completely.