Mazda has issued Bulletin No. 01-010/10 for the above issue:
Some vehicles may experience the coolant level warning light comes on even though the correct amount of coolant is in the coolant reserve tank and radiator. The coolant level sensor float in the coolant reserve tank (A) is deteriorated and absorbs coolant. The float gets heavy, and sinks, causing the the coolant level warning light comes on. As a mass-production change, the design of the float has been modified.
Replace the necessary parts according to this VIN range.
• For VINs JM1FE****** 100000 to 157837 (built before July 1, 2005), replace the tank with sensor.
• For VINs JM1FE****** 157838 to 403405 (built on or after July 1, 2005), replace the tank only.