The water level light is on if that's not it what could it be there is no check engine light on
Could low coolant levels make my 1998 beetle shut off on 1998 Volkswagen Beetle
Not all issues turn the light on. I don't think the low coolant light itself will cause it to shut off, But a combination of that and the temp sensor reading wrong could cause it. Get it scanned anyway just to see if something is there, you might have to use a professional scanner to read history and other modules as well. It would be a NO Code drivability condition.