Windshield washer refill light stays on even when I fill it.
Then I'd say the level sensor on the reserve is either dirty or has failed. You will need to drain the reservoir to replace it. It could also be the wiring to the sensor as well.
Rain X coating the sensor? Siphon the reservoir and flush it and the sensor with lots of water. Be careful not to add any solvent cleaners that could enter the pump and cause possible damage. Only use the blue wash fluid in the future.