Any Idea what this connector might be?
It is a Ceramic Insulator for heat protection - the wires go to the heating element.

EDIT 5-8-2017

As per Ed Beals comment (Thanks for the FYI) - I will make some explanation here . 

Heating elements are exactly that they heat up as the electricity flows through them, they have different ratings of wattage consequently also heat output, How hot they get. Because of this there needs to be a method of protecting the wiring of the circuit from the transference of this heat. 

The heat transferring via the wire into the insulation can melt or make brittle the insulation and thereby create a potential fire hazard and or electrocution hazard. Ceramic Insulators are used to dissipate the heat and prevent this transference that would cause the insulation of the wires to melt or become brittle. 

Over time the heat will cause these ceramic insulators to break  down - constant heating and cooling causing them to crack and become brittle and break. You need to use them in the replacement of your part and in connecting the wires to the heating element - unless you would like to risk the lives of the  occupants of the home to fire.

I should also add that sometimes the heating element itself has this component - and therefore a new element would need to be purchased.