Faulty Light Indicator
There are application targeted components. In the automotive industry, which is where your project should be/is implemented, there are components like Smart Switches, which integrate many diagnosis functions include current sense. You can see on that website that one of their applications is automotive lighting, which is nice.

I know this is way more than what you're probably looking for, but just to get the idea. You could use a simpler/cheaper solution using a MOSFET and a current shunt...

Maybe a better idea would be to monitoring the LEDs' luminosity using a photoresistor for example, but this shouldn't be detecting the sun's ray or other cars' functioning lights :)