I do not have the schematics for a '96. However, I can tell you that when I purchased the '95 seats for my '97, the seat adjuster switch and wiring harness were different so I am thinking you may not be able to use the '95 switch you bought without doing some difficult re-wiring. (I am not sure on this since I don't have the '96 Service information.)
Regardless, I would definitely not recommend trying to hot-wire/jumper anything within the switch. The simple reason is your switch connects to a multi-wire connector and a MEMORY SEAT/MIRROR CONTROL MODULE--not simple connections to get the 12V to where it needs to go. You could easily damage the Module and other circuit devices.
Lastly, my only suggestion, is that if you are familiar with electrical circuit troubleshooting, there are extensive troubleshooting steps in the Riviera Service Manual for diagnosing a seat that only moves one direction. Again, I only have the '97 Service Manual; but even with my electronics background, these procedures looked a bit daunting!
Also, take a look under the seat to see if there are any obvious problems (e.g., connectors not tight, broken or chafed wires, something stored beneath the seat obstructing movement or pinching wires).
Sorry I don't have better news. Maybe a '96 owner out there can be of some help.