FWIW, we've had a couple of these issues with the truck turned off. We've come accross this problem with 40" SR light bars. One of them was mine. Originally, we thought that there was a bad connection within the light bar itself. Bear in mind, the 40" only has one set of wires coming out. So I don't think you're necessarily dealing with a ground issue. LED bulbs are sensitive to voltage input. Even at the slightest change below 12v will make them flicker. That's why you are not having the issue with the truck running. Mine still does it occassionally. But I generally don't have the light bar on unless the truck is running. And, yes, I have it wired with a relay.
The funny thing is, the 40"SR is a combo flood/spot/flood. The furthest flood section from the wiring input is the only one that flickers with the truck off. Is your furthest (from a wiring perspective) Rigid light the one flickering?