Third Brake Light Issues
 

My third brake light started smoking and burning on me while driving. Has anyone else experienced this issue with their Accent? I have been trying to rectify with Hyundai since July and since my car was bought used and warranty not in play I keep getting a run a round. I was just curious if it is a common problem anyone is having or just me. The correct bulb, etc was in it. Seems to be a safety issue that they should repair whether warranty or not. Also, curious if anybody has problems with rpms going low.

There is a little that is unclear here.

Since the third brake light only gets power normally, when the brakes are applied for it to smoke tells us power is getting to it some other way.
What were the conditions when you noticed it started smoking?
What year is your vehicle? To be a safety issue a certain number of cases need to be reported. Until the exact cause is determined, can't say..
Sometimes owners do unusual things and accidentally pinch wires and something like this is not considered a warranty item..
Until the cause is found and corrected ,it doesn't matter by who, that is what is important.
Do you know what kind of warranty you received since you purchased it used?
Maybe the previous owner did something and no one knew, I don't know if any warranty would apply here.
If you would care to supply as much info as possible , maybe we might be able to offer a useful suggestion or two.

It may be related and maybe not, but if there is a short to ground in the wiring , yes it will produce smoke etc., and also cause an unusual load on the alternator which could cause engine RPM to drop down at idle.
There is more here, circuits are usually protected with a fuse to prevent shorts to ground from doing damage. Why wasn't this prevented?

2016 Hyundai
 

I was at a drive through line when the problem occurred since most places if any were not open to walk in. I have seen where other manufacturers have had issues where the bulb gets too hot when braking and don't know if that is what happened. The Accent is a 2016, but I bought used at Hertz in early 2018. It only came with a warranty for 5 years or so many miles which is over. I had a fireman look at it and he said it could have been serious. I am just trying to get Hyundai to see if I replace the parts that burnt if it will be safe to drive. They do not want any responsibility for their vehicle. I had a mechanic look at it and he said all the equipment was correct. Just can't get anywhere and unfortunately my inspection is now due at the end of this month, been ongoing since July. I would just replace it, but not sure if that is safe.

From the info you provided, it does not sound like an electrical problem, but a high heat problem
.If it were me, I would consider doing something about finding a way to let the heat out.