Wiring for JVW5301SJSS hood lights

The wiring for one of the lights for my GE JVW5301SJSS hood had a wire blow out. https://imgur.com/t4UE0ft is what I’m replacing. I’m going to replace it with https://www.amazon.com/gp/product/B07GVB2P2N?ref=ppx_pt2_dt_b_prod_image&th=1 socket and pigtail it to connect to the second light under the range hood. Any idea what gauge wire I need for the pigtail? For the life of me I can’t read what’s on the wire insulation. And the new socket product info isn’t much help either.