WARNING: This page is about a different car, the 2005 Mazda MX-5 Miata, 2004 Mazda MX-5 Miata, and 2003 Mazda MX-5 Miata. However, it is still accessible from the selected car via links, so may be relevant.
Verify that the rubber seal is securely fixed onto the water pump.
Fig 1: Installing Rubber Seal To Water Pump
Courtesy of MAZDA MOTORS CORP.
If not as specified, remove the rubber seal and reinstall it with the bonding agent.