Sometimes the best course of action is the boring one; and if passively sitting listening for rumours is what makes the most sense for the characters to do, then IMO that's exactly what they should do.
Every good GM no matter how committed they are to simulation of the imagined universe metagames in one important way and that is this.
Wherever the PC's are, the fun will follow them.
If we were being strictly realistic, the chances are that characters would have mostly dull and mostly boring lives. Big events would happen elsewhere. The PC's would never be at the right or the wrong place at the right or wrong time. The majority of places they'd choose to go, not a lot of exciting things would happen, and if you tried to make your own "fun" you'd find that challenging as well as most people don't want interesting things happening around them.
But GM always makes things interesting even when the players are being uninteresting. That doesn't mean you necessarily protect them from failure, but that you do definitely make unlikely and interesting things spring up all around them. If they listen for rumors, you give them rumors to listen to.
This is the Batman rule. If in reality you were The Batman, and you went to stake out some alleys in the city to try to fight crime, you might once every few years witness a mugging in progress. In reality, if you were The Batman, you'd always be at the wrong place to stop crime, arriving too late to even witness much less stop acts that take just seconds to transpire. That Bruce Wayne always is where the interesting thing happens is vastly more unrealistic than that he's a billionaire, martial artist detective with an array of high-tech gadgets, the ability to swoop from rooftop to rooftop and uncanny stealth. And yet, it's necessary for a good story so we allow it. We allow it even in stories that are less fantasy than Superhero comics.