A cop can pull you over even if their own headlight is out.
Cops also don't have to have their headlights on at night and cops can also legally hide with their headlights off and they can pull you over for violating laws, even though they are doing the same thing.
As long as the cop or police have reasonable suspicion of some regulatory violation or traffic violation, like a blown headlight or taillights, turn signal lights etc being out, the cop or police can pull you over.
You can also get a ticket for your headlights or headlight being out even if the cops headlights or taillights are out.
It's not right, but that is the way that it is.
My friend was pulled over for a cracked windshield and the cop that pulled him over had an even worse cracked windshield.
He was ticketed and took it to court and showed a picture of the polices cracked windshield that was also in violation.
Luckily he got that ticket thrown out, but it doesn't always happen that way.
But for some violations like the burnt out headlight or cracked windshield you may get a fix it or warning ticket, which requires you to fix the headlight or windshield and have it inspected within a certain timeframe, in which you won't be fined.
Although you can still get a regular ticket for the violation in some cases, and the cost of the ticket can vary by state and circumstances.
The initial stop for the headlight or other light being out is often considered a low level stop, but it also gives the cop, the opportunity to look for other more serious violations like open containers or expired registration.
The officer also has a responsibility to ensure the safety of all drivers on the road, and a non functioning headlight poses a risk.
The officer also has discretion in how they handle the traffic stop, and it often comes down to the officer's judgement at the moment.