Was the replacement GEM new or used? If used I wonder if it's available because someone had the same fault, replaced theirs then sold their bad GEM.
It sure seems like we've already established that the wipers themselves work but for the GEM not energizing the relay (shorting Wiper Hi-Lo pin #2 to ground to energize it). To me that suggests it has to be the switch itself, GEM, relay, or wire/connectors in between. You can use that diagram I posted to check for power all along the circuit, from battery to wiper motor, then focus on the part immediately before the point where power is lost.
If you were to again jumper the Wiper Run pin 2 to ground as I described in post # 16, then you can manually jumper the Hi-Low relay pin 2 (at the wire, with the relay still in) to ground to rule out that relay (if wipers come on, relay is good), or swap it to another relay position again to check that way again.
Next you could remove that Wiper Hi-Low jumper (but not the Wiper Run jumper) and manually jumper GEM pin 22 Pink/Yellow to GEM pin 21 gray/red, which takes the switch out of the circuit and wipers should be working on hi mode, unless the GEM or relay is bad but above you tested the relay. That would leave the GEM or the wiring or connectors to it.
Next I would look into whether the GEM can be non-destructively opened and inspected. I mean your old one.