I can not locate a copy of the wiring diagram (part # 131506800) for your model. There should be one on or in the dryer somewhere. It may be pasted to the rear of the control console or maybe folded up inside of it it. Try to locate it and post a photo of it here.
I looked up the diagram of a later version of that dryer (see pic). There may be some differences to yours so we can't totally rely on it. It does show different colour wires than you described. Maybe the brown wire on your model (to the light) was replaced with a red one some time in the past?
Melville said:
There are three prongs which appear to be the same size (two on one side, one on the other.). There are three wires: red, blue and grey. The terminal on the red wire appears larger than the other two.
I suggest you make sure of the terminal sizes. There are likely either 2 large, 1 small or 2 small and one larger.
Two of the wires will be used for power to the motor, the other goes to the light. When the door presses the switch closed, it switches power to the motor. When the door is not pressing the switch, power shifts to the light.
Someone should test the switch terminals for continuity when static and when pressed. Make note of which set of contacts shows continuity when pressed and when not. Try to determine the common switch terminal.
LINK > How do I test for continuity?
... or look closely to see if any of the switch terminals are marked "C", "NO" or "NC".
The wire that is not connected at either end may have been replaced once upon a time. If it's not connected at the moment, I'd disregard it for the time being.
Dan O.