If you did the check as described (all wiring still connected, key in the run position and wiper switch in off) and the motor doesn't run, you've effectively bypassed the park switch.
Since the motor runs consistently in the low/high settings, a grounding issue is unlikely.
That leaves 2 other possible faults:
A broken wire (kc87/crazy4offroad)
A bad switch (crz4offrd)
Unfortunately, getting to either the switch or the broken wire means you're going to have to pull the steering wheel and go into the upper section of the column (that's where wiper wiring usually fails due to constant twisting motion).
Here - just found these - they are the only decent wiring diagrams for the GM wiper systems I have ever come across. All other W/W schematics are extremely vague and incomplete :
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Wire color codes may not be accurate for your particular year.
Note to moderator: These schematics are good info and should be made sticky.