The rough running is almost certainly due to a separate issue, such as:
* Ignition System Problems: Worn spark plugs, faulty ignition wires, a failing distributor cap or rotor (if equipped), or problems with the ignition coil can all lead to a rough-running engine.
* Fuel System Issues: A clogged fuel filter, faulty fuel injectors, low fuel pressure, or problems with the fuel pump can cause rough running.
* Vacuum Leaks: Leaks in the vacuum system can disrupt the engine's timing and fuel delivery, resulting in a rough idle and poor performance.
* Engine Sensors: A failing mass airflow sensor (MAF), throttle position sensor (TPS), or other engine sensors can send incorrect information to the engine control unit (ECU), leading to a rough running condition.
* Engine Mechanical Issues: Worn piston rings, low compression, or valve problems can also contribute to a rough engine.
In short: The "Service ASR" light indicates a problem with the traction control system. The rough running is a separate problem that needs diagnosis. You should address the rough running issue first, as it's the more pressing concern for the drivability of your car. Ignoring it could cause further damage. A mechanic with experience in C4 Corvettes would be the best resource to diagnose and repair both issues.