Hello and thanks for your question.
Does the light illuminate at the normal brightness with the engine off and the key on and then get dim after starting the engine or is it dim whether the engine is running or not?
Unfortunately this is going to be an internal instrument cluster concern that is going to require cluster replacement to repair. The signal from the PCM to the cluster is sent over the CAN BUS network so there is no stand alone input wire to the cluster for the check engine light. The fact that it works normally until the PCM signals the cluster to turn it off is indicating that the PCM is sending the signal to turn off the light but the internal microprocessor in the cluster is malfunctioning and unable to fully remove the power supply to the bulb.