Is there any way to track down "Sightings" any more?

Solution 1:

As of October 2019, all sightings have an associated PokéStop with them, giving you a rather precise location of where a Pokémon is located... unless you're in an area with no PokéStops.

In the latter case, there is no in-game way to locate the Pokémon unless you have memorized the locations of the spawn points in the area. Before the recent spawn overhauls, it was also possible to use Ingress to find spawn points in Pokémon Go since the same data source (I believe it was XM spawns in Ingress) was used in both games, but I do not know if this is currently the case.