Yep.. that's a flat battery... pull it out and change it before it leaks. These settings are saved in volatile memory and being that the compact monochrome Mac's are hard-power only, when you switch off the switch, these settings are lost if the battery is flat or missing.
I emplore you to if nothing else, to pull the batteries immediately. The Plus has one in the back behind a removable panel near the power switch. It is likely to be nearly 30 years old, and they can leak down onto the logic board if left in. And the Classic II is from an era where Maxell batteries were used in many Macs and these batteries have come to be known for rather violently reacting and basically exploding when they are left discharged or get well past their prime and can demolish a machine very quickly... There is a thread about it on here somewhere. Check out the damage done to my LC475 as an example of what is possible. Unfortunately the Classic/Classic II batteries are not so easily accessible as the Plus... they are a logic-board mounted 1/2AA cell which you have to take the case back off to access. But you really must do it.
I emplore you to if nothing else, to pull the batteries immediately. The Plus has one in the back behind a removable panel near the power switch. It is likely to be nearly 30 years old, and they can leak down onto the logic board if left in. And the Classic II is from an era where Maxell batteries were used in many Macs and these batteries have come to be known for rather violently reacting and basically exploding when they are left discharged or get well past their prime and can demolish a machine very quickly... There is a thread about it on here somewhere. Check out the damage done to my LC475 as an example of what is possible. Unfortunately the Classic/Classic II batteries are not so easily accessible as the Plus... they are a logic-board mounted 1/2AA cell which you have to take the case back off to access. But you really must do it.