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

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

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