[old_tv_nut]

If you can tell it's off center without a test pattern, then you don't need a test pattern.

If you turn down contrast and turn up brightness (black level), can you see all four edges of the raster? I would want to make a quick check that it's a raster centering problem and not horizontal phasing.

I would say, if the raster is off center, then redo the centering adjustments without attention to the white paint. If, looking at the tube, the raster is centered and the picture content is centered, then you have neither a centering nor a horizontal phase problem at the tube; then if the picture on the screen still is not centered, it must be a mirror problem.

summary:
1) center raster
2) check for horizontal phasing problem
3) check mirror alignment