I hooked a trouble/test light up to the fuel sending lead (next to gas tank) on my 1967 Valiant and there was a light, but it slowly "pulsed" on and off. Is this normal?

I'm pretty sure the sending unit is shot, but I wanted make sure the pulsing light was normal. Maybe helped keep the gas gauge needle from bouncing all over the place?

Thanks ahead of time Mopar Dudes!