Drilling broken studs out could be a challenge.
Apply some WD40, CRC, Penetrene or even some good old diesel around the studs and let it soak in for a while before you try to extract any more.
Unfortunately, the tail lights were re-chromed and is around the base of the stubs, welding them to the casing, particularly the drivers side light where three studs broke off. I will have to get four holes drilled and tapped. I could take it on, but would rather pay a shop to do it.