What type of wire should i use to make a jumper on the PCB control board from my dryer?
You need to scrape some protective coating from the trace, then clean with alcohol. You do solder a piece of thick copper wire along that trace so that will touch the relay at the end. Probably you don't even need to buy a new relay, it could be a bad soldering yet from the beginning.
EDIT:
If you have the same issue as shown in the video, then you can simply add more tin to fill the gap. The relay contacts do wear out, this results in arcing, which is high temperature plasma. This temperature is spread over metal contacts to the PCB causing the tin to evaporate and produces the secondary arcing. When you change the relay make sure you won't apply to much heat, it can de-laminate PCB traces.