Right, stars are (effectively) point sources light. But if you take images of stars like the LSST is where you can get the entire sky every few days you'll find anomalous stars that weren't on previous exposures.
I don't know the physics enough to know if a small (earth to neptune mass) blackhole could redirect enough star lights to detectable by an earth (or earth orbit) telescope.
With a huge database containing the time series of the sky you can start searching for unknown objects that stick out because they are a change from the previous exposures for that part of the sky.
With enough data mining of those previous exposures you could find likely candidates and get telescope time to check out where you expect it to be next.
This is similar to how things like Oumuamua and 2I/Borisov were found.
