Take the appropriate action and verify that the warning light turns off.

Taking Action
Message Indicated on DisplayMazda 6 Owners Manual: Fuel Gauge (Without Multiinformation Display)
The fuel gauge shows approximately how much fuel is remaining in the tank when
the ignition is switched ON. We recommend keeping the tank over 1/4 full.
If the low fuel warning light illuminates or the fuel level is very low, refuel
as soon as possible.
Refer to Warning Lights.
NOTE
...
Mazda 6 Owners Manual: No.9 tcs off light stays on more than 4 seconds with ignition switch on
When performing an asterisked (*) troubleshooting inspection, shake the
wiring harness and connectors while
doing the inspection to discover whether poor contact points are the cause
of any intermittent malfunction. If
there is a problem, check to make sure connectors, terminals and ...