Rechargeable LED light bulbs

We supply rechargeable LED light bulbs that have built-in batteries. The purpose is to solve power blackouts, that is, when there is power failure you can still have power by turning on the switch.

We are now facing new challenges with existing circuits which have polarity issues or have motorized device such as a fan on the same circuit with the rechargeable LED bulbs.

Because of these issues when you turn off the switch, the light bulbs do not turn off.

We need help with design of LED driver or electronic that can address this problem. Can anyone help?

How does the existing circuit work?

Mike.
Edit, to detect the switch is closed would require detecting another load on the circuit. Your fan is acting as the other load all the time.