I think we are getting confused on terminology.
SPST - also known as ON/OFF switch, has only 2 contacts
SPDT (center off) - (not mentioned by this name yet) is the 3 position switch I mentioned before, having 3 contacts, ON/OFF/ON. This is also available without the CENTER OFF but is not what the OP wants.
DPDT (center off) - just like the SPDT switch, but has 6 contacts and switches both the HOT and the GROUND, think of this like the ATS on your RV's AC system. This is also available without the CENTER OFF which is often used to reverse polarity, like on a ceiling fan to make it turn backward. Wire the corners in an "X" and hook the motor wires to one end only, you get current flow one direction, then switch it to the opposite flow direction.
The SPST switch will only turn the fan on regardless of the thermostat. It will not turn the fan off if the thermostat has it turned on.
The SPDT will do both.
The DPDT will do both, and in addition will break both wires, which is not necessary.
The switch pictured above is perfect as long as it is DC rated. If it is only AC rated, it will work for a while before it fails. It does APPEAR to be 12v DC rated from what I can see.