Honda Civic 95 starts then dies when key is back in 2nd (On) position

I would love to get some advice on what could the car issue, as I'd prefer to repair it myself, mostly for fun/experience.

Honda Civic 1995 DX Sedan. The issue has happened for the first time around a year ago, but then magically went away until now.

When rotating the key into the 2nd position (On), dashboard lights sometimes are not fully lit up. If I slowly move/wiggle the key towards the 1st (Accessory) position, dashboard lights are then fully on. Moving the key to 3rd position (Run) starts the car without issues, but if I just release the key back to 2nd, the car dies. If I hold the key in the 3rd position the car keeps running. Several days ago I even managed to keep the in 3rd for half a minute, then very slowly release it back to 2nd and the car kept running without issues, which allowed me not to get stranded in the cold and scary Walmart parking lot.

According to multiple sources, it could be caused by a faulty ignition switch. Any thoughts or tests I should perform?

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