You said it’s an LS, so it would have been cloth from the factory with lumbar. Do you have power seats or just lumbar?
On the power seats (and my info only shows the driver side power - mine is power driver side and manual adjustment with power lumbar on passenger) the switch gets 12V at all times through the orange wire.
Pull the harness from the switch and see if you get 12V at the orange wire through the black ground. If not, try it with a ground to the body.
You might try LMCTruck or npdlink.com for a switch, otherwise a salvage yard trip may be in order. Car-Part.com is a good search engine for local yards.
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