I've never actually sat down and done a detailed analysis of shootings vis-a-vis anti-freedom legislation in Congress, but I do know that nearly every time in the past 10 years there's been an anti-freedom bill being debated or voted on, some kind of act of violence has taken place.
As far as legislation being introduced immediately after a shooting, that's simply because all the anti-freedom Congressmen have libraries of legislation they've drafted up ahead of time just for these instances. It's very rare for a Congressman to be unprepared to advance his cause at all times, and drafting a bill isn't something you can just do on demand, even with an army of staffers.
Now, WRT your topic header, the antis don't need a new shooting to renew their attacks - they're ALWAYS on the offensive, it's just that when there's a shooting they get a little more mdeia time. Conversely, if shootings decline in numbers, they'll step up their attacks even more, because they're convinced their efforts are having an effect.