Check charging system light comes on intermittant, 2006 taurus, any speed and any load, battery good, alternator replaced problem persists before and after

Battery Light usually means the alternator is not charging correctly and needs to be replaced. Check charging volts, it should at 14 volts or very close to that number. If the number is low below 12 then the alternator needs to be replaced.

Note: A bad alternator can damage the battery & vise versa

You would need to check the connections on the back of the alternator with a meter.
You should have battery voltage on the large wire and on the orange yellow wire.
The other two wires involve the engine computer which turns the alternator on after the engine starts.

I'm sorry to say it could be the computer.
The computer controls idle speed as well as alternator output.
If the check engine light is on you should get it scanned for trouble codes.

thee wire that does back to the battery runs to starter. check that wire

Loose or intermittent connection at the battery, alternator, or other wire associated with the starting/charging system.

Check your charging system and wiring at alternator..are your battery terminals clean??? is your drive belt loose or need replacing???

check the alternator fuse and grounding

Check for damaged or corroded wires on alternator. Also check connection to alternator, take off and clean. Alternator may be on it's way out. You might want to get it tested at garage or replace if problem persists.

Where did you buy alt,have had several issues with alternators from auto zone,But check belt tention and idle speed.

sounds like a bad alternator the rotor may be flying open at high rpm