There are a couple of things I question about your drawing. I should say "that make me nervous".
The most significant is the jumper across two points. The switch, if I am seeing it correctly, has two lugs (jumpers, bars, whatever) that switch between straight across and crossed. FWD is one way, REV the other. The lugs? will change shorts from FWD to REV.
Now, without actually seeing how the switch moves, I will proceed through what is necessary. The first thing is to determine which wires are which at the motor. A multi-meter is the most well known tester, there are many ways to check continuity. Use the "ohms" scale, Rx10 or Rx100, to ring out the wires. There will be two distinct windings, one of a relative fixed resistance, one with a tapering over time. The former, the run winding. The latter, the start winding.
The wire colours are
relatively meaningless. As in, they will vary from motor to motor. I am going to
assume the black pair to be the run winding and the red pair to be the start winding. This
may or may not be the case. But will do for my explanation. As long as one winding is reversed
relative to the other, it will reverse. So, make the continuity test and determine for sure which pair is a winding.
Do that first, by whatever method.
Once that is done, connect one black wire to the neutral. The WHITE wire in the line cord. This connection is not connected to the switch at this time. It is a stand alone connection. The other black wire connects to the terminal of the switch that closes
only straight through. An ON-OFF switch. The other side of that switch connects to the LINE side, the BLACK wire of the line cord. This will leave an X-II connection on the switch.
The four connections left will be on the diagonal. In REV, they make up one way. In FWD, they make up the other. Connect the RED pair to half of this. The other half connects to the line cord. This will reverse the winding, depending on which way the switch is thrown.
UPDATE
Sorry for the interruption
....
The enclosed photo is from a plastic, Chinese made drum switch. It
does not match the Grainger switch but will illustrate the connections. The important issue here is to reverse one winding relative to the other. And to open both windings in the OFF position.