DIC message, "Check Coolant". Surge Tank Coolant level indicates full upon removing cap. There is no heat and the heater core is cold. How to circumvent surge tank & add coolant to engine radiator?

The problem is most likely the sensor itself, as the tank is mounted high up the coolant will fill the radiator from the recovery tank. You can unplug the level sensor and check to see if it is closed with the tank full if it is closed then the sensor is defective. Question: Assuming the level sensor is NOT defective, what should the coolant in the recovery tank do when I unplug the level sensor . . . stay in the recovery tank or run out?