Journey
Cruise
Once they have been accelerated to a speed of 25 astronomical units (AU) per year, SGL probes face a lengthy, lonely cruise to the SGL focal region.
How lengthy, exactly?
Very likely, when the first SGL probe is launched, it will be the fastest object to date made by humans. It will cross the orbit of Neptune in a little bit over a year (it took Voyager 2 roughly 12 years to get there.) After aboute 6 years, it will surpass Voyager 1's present-day (2022) distance record, which took Voyager 1 nearly half a century to achieve. And then it will continue to travel in deep space, in the outskirts of the solar system, for many more years, approximately 25 years in total.
The SGL probes' trajectory will be designed to ensure that when they finally reach the necessary distance from the Sun, they will be in the vicinity of the optical axis of their intended target. This is, of course, very important. It does not help to be 650 AU from the Sun if you traveled in the wrong direction! Fortunately, in addition to the usual navigational aids, SGL probes will also be able to "keep an eye" on the host star of the system where their intended imaging target resides. This is not important early on, because we know how to navigate spacecraft by other means, including radio navigation using NASA's Deep Space Network. But at the end of this part of the journey, it will be light from the host star that will begin to guide the probes as they transition from cruise to the science phase of their mission.
"Arrival" at the intended target region does not mean that the spacecraft will stop. Indeed, they have no means to stop; that would require far more fuel than they will likely carry. And there is no point in any case. The nature of the SGL is that (at least up to about 2,200 AU) the farther the probe is, the better. Light from the target exoplanet appears as an Einstein ring around the Sun. Yes, this Einstein ring shrinks with distance, but the Sun shrinks more, and therefore, the apparent separation between the two increases. The end result? An Einstein ring less contaminated by unwanted light from the Sun and the solar corona. So the spacecraft will continue to fly out of the solar system even as they begin scientific observations.