I have an old black and decker 3/8" drive electric drill. I have a 6 pin dpdt on-of-on switch. How can I use this switch to reverse the drill rotation without flipping the forward/backward lever on the drill?

 

Remove the reversing switch on the drill and attach the DPDT switch in its place.

 

AFIK, those motors are wound-rotor, wound-stator. Reversing requires flipping either rotor with respect to stator or vice versa...

 

Use the switch to reverse the wires to the brushes.​

 

Use the switch to reverse the wires to the brushes.​

The brushes feed the rotor...

 

Remove the reversing switch on the drill and attach the DPDT switch in its place.

 

Remove the reversing switch on the drill and attach the DPDT switch in its place.

 

Here's the drill internals....not sure how to get rid of the trigger and have it operate solely on a toggle

 

Max, you lost me with the bridge suggestion. Another problem may be that the drill could be variable speed, ie triac control.

 

Actually forget that, I jumped the gun a bit.
Max.

 

As others have said, it is a Universal motor so the field or the armature has to be reversed WRT the other.
If you notice the left hand stator winding goes to the left hand brush, this conductor would have to be cut and each end connected to a conductor to enable the reversing of the field to the rotor.
It may not be worth the hassle.
Max.