Just to put your mind at rest the blackening on the conector is most likely some water proofing Mazda put on to protect the connection. One sees this question of is my connector burnt all the time on MX-5 forums see third post on this link for a photo :- Passenger side dipped headlights and side lights failure - #2 by Foxcompaq
Sorry I cannot help with diagnosis of the fault with your paper weight, hope you find a fix soon.