Problem with back-up lights

Hey everyone,
I have a '94 Rodeo 2WD V6 with manual transmission, and I'm having a problem with my back-up lights. They won't come on when I shift into reverse, but
they will when I'm in either 3rd or 4th gear. I've had someone tell me that it's probably a problem with the back-up light switch. The previous owner had the clutch replaced before I bought the Rodeo.
Any suggestions will be appreciated.

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