If the wiring harness is not flopping around in the cabinet with bare ends (put some wire nuts on the ends?), then you could power up the machine and activate the pertinent switches/buttons.
Since you need to watch/listen to the contactors while doing this, you may need to override the cabinet cover interlock with a jumper wire.
There is an excellent chance that you have pairs of contactors, which are mechanically interlocked, to avoid multiple choice activations.
Set the machine to Low, Forward.
When you activate the Start/Stop switches on Low, Forward, you should be hearing clunking noises in the cabinet. Which contactor(s) is that contactor when Start/Stop is activated? Mark that contactor(s) as Start/Stop Low-Forward .
When you activate the Low/High switch, which contactor(s) is activated? Mark that contactor as Low/High.
Set the machine to High, Forward.
When you activate the Start/Stop switches on High,Forward, which contactor is activated? Mark that contactor as Start/Stop High-Forward. Most likely, the same Start/Stop contactor as used for Low, Forward.
When you activate the Forward/Reverse switch, which contactor(s) is activated? Mark that contactor(s) as Forward/Reverse.
Set the machine to High, Reverse.
When you activate the Start/Stop switches on High, Reverse, which contactor(s) is activated? Mark that contactor(s) as Start/Stop High-Reverse. Most Likely, the same Start/Stop contactors used for Start/Stop as the two previous Start/Stop tests.
If you are having trouble with this procedure, find a math major that is fascinated with combinatorics.