Engine Light keeps flashing & pistons sound like they are coming thought hood on 1996 Mercury Cougar

At idle, the motor has a thump when the pistons fire.
Sounds like a piston misfire.

The engine light may be something else.

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2 answers
If there is a low sounding knock which increases when you idle up a bit you most likely have bad rod bearings.
Try to retrieve the diagnostics trouble codes from the computer to have an idea why the engine light is flashing.