TL;DR - I don't know, but there are some hints.

As Gaia wheels across the sky, the science team takes note of anything that wasn't like it was last time they visited. Some of these events are asteroids or comets, but quite often it's just a distant source that has changed significantly in brightness. They publish these events as Gaia Alerts. Most of these are candidate supernovas (SN) or cataclysmic variables(CV), but a few are objects that have declined quite a bit in brightness. Of course, there are lots of reasons that the brightness of a source can go down, so this doesn't mean that they're anomalous dippers like Boyajian's Star. For example, R CrB variable stars can have fast, dramatic dips, but they are fairly well understood, as are Young Stellar Objects (YSOs), which can exhibit frequent dips.

I made a list of the faster dippers in the Gaia alerts. The ones highlighted in yellow are the ones I think might be best candidates as analogs, but all need more study before we could conclude that.

In addition to the Gaia data, there are other data out there that could be mined - the Catalina Real Time Transient Survey, for example, which had a real nice light curve for Gaia16asp, for example, showing earlier dips.

So, this is something amateurs can do that is not a waste of time, necessarily. Once we have candidates, we'll need some professional help (in more ways than one, perhaps), since only spectroscopy can settle the issue.