Hmm, most OBDII code readers will read most of the critical ENGINE codes, after all, that’s the whole point. There is not much on the little 1.4 engine to monitor so an OBDII reader should find why the light is on. As Missing Lincs said have you tried reading the codes now the light is permanently on?
I am trying to think of what might cause the engine light to come on but the engine runs fine. Non-critical systems like the 02 sensor heaters don’t bring on the light because…well…they aren’t critical. You might have a downstream O2 sensor out but I’m just guessing. If it brings on the engine light you should be able to read it with a code reader.
Most parts of the engine management system are needed to run the engine but the downstream O2 sensor just monitors the catalytic converter and while critical to the anti-pollution system, it has nothing to do with the performance of the engine.
Having said that I think the engine light is incidental to the car stopping. I still believe the major problem is fuel related and the light is something else. However that assumption is based on the light not coming on as the engine stops.
When the engine cuts out while driving, does it slowly (1-2 seconds) loose power and die or just drop dead instantly?
Unfortunately intermittent failures are a pain. Until they fail (again) the system will typically not give any hints of the problem and so are difficult to diagnose.
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