Philip,
There are four basic types of DC motors - Series, Shunt, Compound, Permanent Magnet. The Series type is AC/DC, is sometimes called Universal, and is seldom found in sizes above about 1/10 HP. Your motor is compound wound, and is the only one of the four that should have 6 wires. The permanent magnet type only has two wires. The series and shunt will have two if they are not intended to be reversible (the four wires are tied together internally) or four if they are reversible.
The two-wire controllers that you have found are most likely all for permanent magnet motors. They will run the other three types but the Reverse switch on them will not reverse the motor. The one that you would want should say for compound wound motors. If all that you can find is one for shunt wound motors, this will work but you will have to outboard the reversing switch.
Two wires will go to the armature. Two will go to the series field. And two will go to the shunt field. I can't really think of a logical reason for yours to have 4 studs and 2 loose wires instead of 6 studs. If the motor is going to be reversible, you have to flip both field windings. Below are stylized wiring diagrams and schematics of the first three types.
If you cannot ID which of the three windings the studs and wires go to, using an ohmmeter, the series winding and the armature will have very low resistance. The shunt winding will probably be several thousand ohms. To differentiate between series and armature, pull one brush to ID the armature.
Note that to reverse the compound wound motor, you either reverse both windings or the armature. Reversing the battery will not reverse the motor.
Also, the drawing below, which originally came out of a WD training publication, had an error on the shunt and compound wiring diagrams. I corrected the error by moving the battery connection to the right end of the shunt field winding from the positive to the negative battery terminal.
Robert D.