Geyser gazers are the people who make geyser eruption time prediction possible. They are volunteers, most of whom belong to GOSA, the Geyser Observation and Study Association. Many of them also subscribe to a mailing list, which is associated with GOSA but not part of it. Some are professionals, but most are enthusiastic amateurs. All of them are passionately interested in geysers, and spend as much time as possible in Yellowstone observing, communicating, and recording geyser activity, in conjunction with the park rangers and the visitor center staff.
Since most geyser prediction is predicated on average intervals, lengths of eruptions, and other, more complicated algorithms, knowing when and for how long a geyser erupted is crucial to being able to predict what it will do next. Making a good educated guess (geysers are not faucets) as to what a geyser will do next makes it possible for more people to see it.
I don't lay claim to being anything more than a very beginning apprentice gazer, and I can't spend nearly as much time in Yellowstone learning more as I'd like. But I do have a walkie-talkie (gifted to me by a very good friend), and I have had the excitement of being the first to call in an eruption.
I called this eruption of Daisy Geyser
It's all terribly addictive [g].
So the next time you see someone walking around the Upper Geyser Basin with a walkie talkie and a notepad, be glad, because that next eruption of Grand? Just may have been predicted with their help!
Obligatory Grand Geyser photo (it's my favorite)