2019 BMW X2

My battery died. After a AAA jump, the car started fine but the right-rear-taillight-signal malfunctioned. It was working fine prior to the battery dying. I purchased a new battery and the mechanic said my right-rear-taillight was getting an electrical signal and the bulb work, but I needed a completely new taillight component ($300!) because it still was not working. While researching parts, I came across a YouTube 'fix' that showed that within the lightbulb compartment, there was a little piece of plastic that was MELTED preventing a mental piece on the lightbulb casing from touching the metal on the compartment preventing the light from coming on. My mechanic sanded down the melted plastic so the two metal parts could touch, and low and behold, the right-rear-taillight-signal worked just fine. Now I don't know if a battery failure could cause an electrical shock to this little piece of plastic but in the comments on this Youtube "fix", this same scenario happed to someone else with an X2 and their battery died and the right-rear-taillight-signal immediately failed. Is there a connection? What caused that little piece to melt??