Circuit Board Connector Pin Broke

That isn't where a orange wire goes. That is a gauge sender wire. Oil or temp? Gray or voilet/purple?
The post that orange wire goes on can't be seen under your red circle drawing.
Put a ring terminal on that wire. Attach it on top of the speedy nut with a toothed washer and hex nut just like those on your amp gauge. It's #10-32. Any hardware store should have. Home Depot, etc.. will have 4 to 10 count in small packages.