Every point in the sky is on a possible orbit (or on infinite orbits?), so you are not really reducing the problem space.
Our planets' orbit do tend to be somehow aligned, so you could make the (possibly wrong) assumption that the 9th planet is also somehow aligned. This might reduce the search space by 50%+.... but even then you'd still be several orders of magnitude off by the precision needed to go looking for it.
Saying a planet in our solar system is in orbit around our sun is like saying a shipwreck is underwater. It doesn't narrow down the search region at all. And worse, we don't know it's in orbit around the sun as we don't even know if it exists.
But if you suspect it’s a planet, you know it’s in orbit around the sun. Feels like something we can track.