As stated in other answers, there isn't really a good natural candidate for this object.
But if you are willing to permit an artificial object, then there is something that comes close:
A large interstellar probe
Launched many thousands of years ago from a distant star-system, the interstellar probe is initially invisible, coasting through space at a measurable fraction of the speed of light.
Far out from your solar system it ignites its engine and begins to decelerate. In order to journey between star systems it would need an absurdly powerful engine, perhaps powered by nuclear fusion, antimatter, or some exotic physical processes that are currently unknown to us. Even so it would take a long time to decelerate. While it does this over months or years, it's engine is visible as a steadily brightening star in the sky. It would not appear to move much, as it is moving towards the solar system it is being observed from, meaning there would be relatively little angular deflection.
As it decelerates into the solar system, passing inside the orbit of comets and outer planets, it will now be moving much slower, and following a trajectory around the star a bit closer to that of a planet. Hence it will appear to wander in the night sky, but in a predictable manner.
Once it has decelerated into the inner solar system, it has slowed down to interplanetary speeds. At this point, its programming changes, and it begins a survey, flying from planet to planet on brachistochrone trajectories. It would appear to move between other planets and asteroids, and although it's trajectory would be predictable from night to night, where it goes after each stop might not be.
Perhaps during this phase, it journeys to a gas giant, and deploys cloud-scooping drones to refill its propellant tanks.
After it has finished its survey, it begins to accelerate again out of the solar system, becoming dimmer and slower, eventually appearing as just another star in the sky.
There isn't much of a reason for it to repeat this in a cycle. However, suppose there was a software bug that had escaped testing and QA. The probe inadvertently wipes its memory of the survey data, and loses track of it's position. It could decelerate and return to the same star system, thinking it has arrived at its next survey destination, repeating the cycle again and again.