I'm not aware of any "engine exhaust fault lamp" as an individual tell-tale indicator, but the EML (Engine Management Light), CEL (Check Engine Light) and other derivatives, will be illuminated on the instrument cluster, due to fault(s) identified within the ECM (Engine Control Module), PCM (Powertrain Control Module) and other similarly described ECU's (Electronic Control Units)
Is the light you refer to shown in this below image?:
View attachment 113067
Regards.