Dash Lights Come on then Off - Car drives fine (96 850)

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12.1 volts on a resting battery is really low.

Let's get some more info. How old is the battery? Take a pic and report name brand and numbers and we can figure out its age here. If it more than 3 years old replace it.

The ignition switch isn't hard to replace but use a new one, not a junkyard. I have a spare one if you want to diagnose