With looking at one picture my guess is circuit breaker. 16 g wire is only good for about 20 amps max so that breaker shouldn't be over 15 amps or so. I would replace it with a type 3 manual reset. Those automatic types are fine until you have a fault that makes it keep tripping. If it continues to trip, it finally goes into melt down and welds to the ON position and takes out the wiring harness. Not real common but I have seen it a few times. It's cheap and easy to just upgrade to manual reset. I would agree to find out what is on that circuit before determining the breaker size.
The reason another 16 gauge wire may be on the side with the large wire is because they ran a hot wire to another device.
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