This is not melting, this is high voltage arcing. Electrical tape is not really suitable for insulating high voltage wires. You need to unwrap it, clean the wires and splice them properly. Here is how I usually do it:
- smooth solder joint with no sharp edges;
- clear silicone sealant;
- heat shrink tube;
- more silicone sealant;
- one more heat shrink tube.
Good luck, and welcome to this great forum!