2006 Corolla No crank No Start problem demonstration.

This video is showcase a very weird problem that I have since I bought the vehicle. Occasionally (about once every other day), the car won't start-there's no crank and no start-unless I keep trying to crank it while shaking the car (slamming my back onto the seat). To address the issue, I’ve replaced several parts with new ones to rule them out as potential causes, including the starter, Park/Neutral Safety Switch, starter relay, ignition switch, and battery terminal.
While trying to figure out why shaking the car allows it to start, I checked for loose wires, but everything seemed secure. I also tried wiggling the harness under the steering column, but that didn’t help. I wiggled the battery cables, but that didn’t make a difference either. I inspected the ground points in the engine bay that I could locate (not sure if I located all of them), and they all appeared to be firmly secured.
Does anyone have suggestions for tests I should perform to narrow down the cause?