Water Heater noise and odd wiring

I believe that is a one-time thermal fuse. The noise is probably frying water if that is actually where it is coming from. The insulating sleeve is to keep it from shorting out against something. The body of the fuses are metal and at line potential. Kind of dangerous if left bare. It should not be in the position it is where water can get trapped in it (even from condensation). I suggest you use a razor blade to make some small slices in the tubing so moisture can easily evaporate and/or cannot get trapped. You might also want to bend the fuse wiring up so the fuse is above the two ends of the tubing. A whining noise could also just be noise of water sizzling against the heating element in the tank. Home water heaters can also do that but their bigger size makes the noise harder to hear unless you put your ear up against it. You said the noise occurs with both forms of heating.. are you sure the electric side is off when the gas is heating the water? Both can be on at the same time if you are hooked to shore power (heats water faster). For test purposes, you could remove the fuse from the circuit (it looks like it's a plug and play set up) and plug the brown wire right to the terminal and see if things are quiet. Put it back, though!