Lack of vertical deflection in a compact Mac is almost always caused by a poor connection. Resoldering (with fresh solder) the yoke connector should be performed as a matter of course. After doing so, pull out the cable and inspect the mating surfaces for oxidation, burning, etc. Repair/replace as necessary.

In very rare instances, the vertical deflection IC blows. IIRC, it is still a TDA1170 in the Classic II. This chip is very common, and probably still widely available. But resolder the yoke connector first, and see where things stand at that point.