My first scope was not a Tek (it was a Kenwood of the 80s) and, like some Teks, it has a feature that is known by the name "Auto-Focus".
The Kenwood had a problem that was exactly as what you described and it was occurring due to leakage on the components of the Aut-Focus DC restorer.
*IF* your 2465B also have an "Auto-Focus" circuitry (I`m not sure, I don't have a 2465B schematic at hand nearby), the problem may be there.
Look for an auto-focus circuitry on your scope and, if it's present, it will surely be consisting of a low voltage amplifier (quite similar o identical to the one to the Intensity control) and a DC restorer (likewise, identical to the one on the intensity control).
The DC restorer circuits, of both the Intensity control and the focus control, are quite sensitive to leakage.
=> Look for leakage on the DC restorers' diodes and capacitors.
=> Make sure the area is clean and as free as possible of H.V. soot. Soot can absorb moisture and the DC restorer will leak until the scope is heated, when the soot will dry and DC restorer performance is recovered... until it cools down again.
=> Check the output waveform coming from the auto-focus amplifier during the problem, and after, to see if the problem may be coming from the amplifier itself.