The dimming of lights when your furnace is off could be due to fluctuations in voltage caused by the electrical system in your home. When the furnace is turned on, it requires a significant amount of electricity to power its components, which can cause a drop in voltage available for other devices, such as your lights. As a result, the lights may appear dimmer when the furnace is on.
Conversely, when the furnace is turned off, the electrical load on the system decreases, leading to a slight increase in voltage available for other devices. This increase in voltage may cause your lights to appear brighter when the furnace is off.
To investigate this further, you may want to consult with an electrician who can examine your electrical system and identify any potential issues. They can ensure that your electrical system is properly wired and that the voltage fluctuations are within normal ranges.