I tried to dip the captain's fob in a bucket of water but the engine did not shut off. Why?

The 1st Mate system will not shut off the engine if the fob is only exposed to rain, splashes or a bucket of water.

The range in air will vary depending on the wireless surroundings of your boat from at least 50 feet, but if you fall into the water as in the ocean or a lake, the 1st Mate system will detect a man over board situation and stop the engine. In this case the range in air does not matter and even 3 feet between the hub in your boat and your wearable fob will kill the engine when the fob enters the water.