Well, I chose to look for c/8 ships because it's the fastest possible diagonal speed that hasn't yet been found and has glide-reflect symmetry (which allows searching for an object with half the period)
Slower speeds get harder and harder to find, and if more people are looking for a speed then it is more likely to be found. Once a c/8 ship is found I'm sure people will be looking for c/9 and c/10.
Now I'm wondering if there is a spaceship with only one or two switch engines. There probably is, but the question is how hard to find it would be.