Only one post gave the right answer after a whole lot of reddit and ED forum searching, and it wasn't even in English!
Push is essentially guaranteed to be found at "Irregular Marker" POIs, BUT only at those that have a Threat Level >=1. Sites that are called "Irregular Marker" but don't give a threat level or say threat level 0 are the wrong kind of site.
That said, DO NOT try to go looking for Irregular Marker sites. Some have said there is a particular BGS state and/or economy type and/or government type in order for a system/body to have the right kind of Irregular Marker site, however, there is a much easier way to find them:
I'm not sure if only certain BGS State/Economy/Government stations have them, but what you want to do is grab the on-foot mission type with a title like "Recover <item> from the hidden cache". That last part, "hidden cache", is what's important. It's an illegal salvage mission, however, there's a change like always that there will be no scavengers or skimmers (that was the case with the one I grabbed). Those mission types will (I think) always bring you to a threat >=1 Irregular Marker site. No searching needed !
