Curate, connect, and discover
Okay, but in The Batman, Gordon seems like the only cop that’s ever glad to see Batman there? Maybe Martinez too, but everybody else is very standoffish, suspicious, and just really don’t seem to like that there’s an adult man in a bat mask and a cape walking around doing their job better than they are.
Which leads me to believe that Gordon not only came up with the idea of the Bat Signal, but he suggested it and fought for it. Went to the head honchos with a 50 slide powerpoint presentation on why it was a good idea. Argued with his superiors that not only was the Batman a good presence, but that the GCPD needed a way to get in contact with him and summon him to crime scenes.
Imagine he lights it up for the first time to test it out (without telling Bats), and Bruce sees it and immediately hauls ass to track down where the source of it is. He arrives there as Batman, and Gordon is standing there with a stopwatch and four other cops. And Gordon is just like “BOOM! I told you it would work! Eat shit! And in 7 minutes flat! Pay up!”