Sounds like some wires rubbed through or are cut on a metal edge and are shorting power to places power/voltage is not intended to go. The static will be from arcing to whatever damaged the wires. Since it appears related to battery wiring that is a good place to begin the search. Slight other chance - a wire was terminated improperly and a single strand has been deflected to a nearby conductor at a connector. I say slight because that may make electrical noise and gremlin behavior, but will tend to melt before creating a brown-out.
It probably shows up for a limited time when the engine starting torque is highest and that torque is enough to twist the cabling or engine mounting the 0.001 inch required to close the electrical gap.