Barry,
What you seeing is a good tube. At high brightness, the phosphour is being struck with a large amount of electrons exciting the phosphour around the ones being struck causing them to glow. Double-peaking is when the tube is weak and the brightness will be fair, low then fair again as the intensity is from low to max. The focus is usually out not matter the position of the focus control. The tube will also be slow to show a trace when turned on.
Mark
