Hmmm.
I have a very similar scope. If yours is like mine, there is a set of concentric controls with the markings "Holdoff" and "Level", with "Lock" and "Norm" on the lower left. Refer to photo and tell me if yours is the same or similar. The holdoff, lock and norm words refer to the inner control (furthest from the panel, smallest, top, whatever), the holdoff, which should be turned counterclockwise until in locks in the norm position which is minimum holdoff. Then you should forget about it.
The "Level" refers to the outer control (closest to the panel, largest, bottom) and is the trigger level. The normal position, if there is one, is centered, which represents a zero crossing trigger. Immediately above it is the slope switch, which determines whether the trigger happens on the way up or the way down.
Let me know what other equipment you have (sig gen, etc) and I can suggest some ways to track down the problem. A photo of your panel and how it is set might be helpful. I'm still not clear on "the signal tracking right" but for now I'll assume you are in the AUTO sweep mode and the trace is not steady in one spot but is "walking" (or running) one way or the other. If you really tried a lot of signals, I'd expect it to occasionally walk either way but mostly just be blurry.