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Just to be sure, remove all four wires from the new switch and see if the red light is still on. Assuming it is, then take a look at your fuse box and see if, by any chance, there is some piece of crap of some sort over on the passenger side of the passenger side fuse block that is jumpering the second fuse to the third fuse. Assuming there's nothing, and your light is still on, put someone in the driver's seat with instructions to yell if the light flickers or goes out. Then, start wiggling wires gently. If that fails, you will have to trace the #3 fuse circuit to see where it is getting the hot feed when the ignition switch is disconnected.
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