Notification when GFCI trips

I was thinking of a low-tech solution, that works when you are on the premises. The idea is to wire in a 120V lightbulb socket with an LED bulb. The hot side goes to a non-GFI breaker. The neutral side goes to the hot of the GFI breaker. When GFI breaker closed, both are hot and light is off. When the GFI breaker trips, current flows back through the (in my case) sump pump motor, which is a much lower impedance than the LED bulb, and the bulb lights. I’d place that apparatus under the eave of the shed where the breakers are and can see from the house. Would that work? I have heard that GFI breakers can do weird things if the hot side has any voltage on it when it’s tripped.