looked at your video........ that garbage looks like power supply ripple. either electrolytics or voltage regulator or both are bad, so check the supplies first, if that's not it, then proceed to cleaning pots and checking the amps for offset. the best way to find ripple in a DC power supply without a scope, is with a meter set on AC volts. most regulated power supplies should have less than 1% noise and ripple on them. so for a 100V supply, there should be less than 1V noise and ripple after a regulator and filter
before you clean any internal pots or caps, mark their position.
sounds like your DC balance of the final section of the vertical amp is the problem, since both channels do exactly the same thing. you could have one side of the deflection power supply out, or something amiss in the section of the vertical amp after the front channels get switched in. most scopes have the main vertical amp and the channel input amps, which get fed through a switcher that allows you to either select one channel or the other, or switches them electronically, either chopped or alternated. your problem is after the switcher circuit (unless you're missing a supply rail to the input amps). so the first place you want to look is the supply rails of the input amps and the supply rails of the final amp. if the rails are ok, switch to channel A and put the position pot in the middle, and use the input switch to connect the input to ground. then begin checking amplifier outputs for DC offset from the input amp, through the channel switcher, to the final amp, to the deflection plates. most scopes uses dual supplies (=/- rails), but if the scope uses a single ended power supply, then you're looking for half the supply voltage to be the "zero" reference.