pull the switch and check its position / contact configuration to confirm your "analysis". The switch likely is a "double pole switch"... basically a center contact for the ground wire (or battery depending on wiring) and two "poles", which contact the center when "toggled". It could be a different configuration like car windows which tend to actually switch both negative and positive around at the same time... usually because there is only two wire feeds to the responding motor which is DC which in most cases don't care on which contact it receives the voltage / grounds on.
A "three wire" motor maybe be slightly unusual.