How do you know when your alternator is going out on your car?

take to parts stor like autozone ect and have a load test done to check for battery/alternator issues.

Signs might include dim lights, check engine light, squealing sound, engine stalling, others. This takes some diagnosis:

https://shop.advanceautoparts.com/r/advice/car-maintenance/how-to-diagnose-a-failing-alternator

Should have a gauge or 'idiot light' that warns you that they system is not charging, other than that your lights would been dim.

I can't say 100%, but as far as I know, there are a number of lights that come on when starting a car. The alternator light is one of them. Is it possible that you never noticed it before? On my car, the check engine light comes on, the engine trouble light comes on, the seat belt light comes on, the air bag light comes on, the abs brakes light comes on and there are probably others.
I think what you are seeing is normal.
Do you have any problems? Is the battery dying? Is the car stalling? If not, you are probably OK.
Gary

i would crank the car open the hood and loosen the positive battery cable ,if the car turns off the alternator is bad ,the blinking of the charging system is the first sign of the alternator going bad

It could be the alternator is faulty. Usually when alternators go bad, they give you warning signs like this.

Water pumps leak when they start going bad... it's kind of a warning sign before they let loose. So there's a good chance that you're right.

could be alternator light

Have your alternator checked. Most auto supply places do this at no charge. Multiple dashboard warning lights usually indicate alternator problems.

That may be a sign of a bad alternator. start you car and take the positive batter cable off the battery. If the car dies replace the alternator. That is a really good sign that your alternator is bad.