This may not be as easy as putting in a SPDT switch, you really need to know what the capacity of the circuit you are wiring into has, as now you could be asking it to provide power for both lights at the same time. Adding a relay would be the easiest way to attach to the existing circuit with minimal power draw. After that you need to understand if the current switch is switching the 12 Volt Power or a ground going to the other side of the light source. I would call one positive sourced and on negative sourced. I have attached some drawings of each, that should help explain, I did throw them together rather quickly so, if it doesn't make sense please ask, I may have screwed them up. In both cases the existing switch is used to control a SPDT relay. The new light will be controlled by the Normally Open input of the relay (87). We use a standard SPST switch going to the Normally Closed input of the relay (87a) Note: this switch must be capable of handling the current load to the new light (even if it is negative sourced) . In both cases the existing circuit only has to take on the added current load of the relay coil instead of the new light also.
hope this helps