No, there is no internal control memory, this is a very basic 70s amp.
It is normal for both lights to be on without the footswitch. They are on because both channels are live. If you plug into the automix jack, that feeds both channels, and if you have the footswitch, you can chose one channel or the other or both.
It is not normal to plug into one channel and have both still working, as in the other channel controls your sound too. That would only be normal plugged into the automix jack.
My suspicion is that the automix jack is the problem though. It has a grounding contact in it, that grounds the inputs when the jack is not in use. If that contact is bent or dirty, then the two channels do become wired together. I think that jack needs service, cleaning, or at worst, simply a new jack there.