Some not so great memories of used and abused engines here but the fact still stands, under normal ops modern final stage turbine exaust may glow due to temp/metallic alloy.
The only reason otherwise would be excess fuel in the turbine section during start, engine failure or after burners installed in mostly military aircraft.
Another note..EGT is only relevant to the position the engine manufaturer decided to install the "rakes" or sensors at. The exaust gas temperature varies throughout the T-stages and tailcone.