When I got my '93 it had the same problems. Used a hose to duplicate rain. Drivers side vent/kick panel assy. was leaking at the seal between it and the sheet metal.
I bought a new seal and used a very generous amount of black RTV on both sides of the foam seal. Probably will have to break kick panel to get it off but no leaks. Passenger side had two problems. One was A/C intake to sheet metal seal, same basic problem as driver side but would have required removing the A/C evaporator and heater core assy. to fix the same way so I did what 3dracer did and it stopped. The other problem was at the lower corner of the windshield seal. I tried different RTV's but that didn't help. Took it to a windshield guy and he removed the glass and resealed it completely using the same gasket. The leak was at a spot where two cab sheet metal sections were welded.
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'93 W350 Club Cab, Bright White, 5 sp. , 132K, Factory Options: LE, 4. 10 Limited Slip, 7600 lb. rear springs, tachometer, front stabilizer bar. Mods: Banks stinger plus, Linex bedliner, 25,000 lb gooseneck ball, 10,000 lb receiver, Tekonsha brake controller, POWER WAGON injectors-WAY faster than stock!.