Hello jeb3558
This type of connection is common for shaded pole type motors, but at 1/2 horspower, this is not likely.
If it is not a shaded pole motor, then it could also be a universal motor (with brushes) again not likely if it is for continuous running.
Logic would suggest that it is an induction motor, and if it is, there must be a start winding.
There are a number of configurations for the connection of the start winding in a single phase induction motor, some of them are represented here :
In order to reverse the rotation of a single phase induction motor, you need to identify the start winding and reverse its connection. The four connections that you have identified so far, are connections to two run windings, each wound for 110 volts. You connect them in parallel for 110 volt operation and in series for 230 volt operation. Thes two windings are both run windings, neither is a start winding so do not reverse either winding relative to the other.
I suspect that on of these run windings, will have an internally connected start winding in parallel. The start winding may have a series capacitor and may also have a series switch which operates when the motor reaches full speed. If there is no capacitor, then there must be a switch.
You will need to partially dismantle the motor and trace the connections that go to terminals 1 2 3 and 4 and look for the parallel winding with a series component (capacitor and/or switch). Once you have located this winding, reverse its connections, and the motor will run in reverse.
Best regards,
Mark Empson