How do I replace these metal pieces from my instrument panel?

Why the pins weren't soldered from the factory... If the pin pulls away from the board it will peel the copper trace off the board with it.
Not all models have circuit boards. So follow copper trace from broken pin to where it goes. If it goes to a lamp socket, anchor and solder replacement pin for the harness connector is easier/more practical than alternate lamp socket with wires.
Where copper trace goes to a gauge post, you can remove that wire from the connector and put a ring terminal on it. Place the wire on that post. Original speedy nut first, then your ring terminal followed by toothed washer and 10-32 hex nut just like those on your amp gauge. Home Depot has them in little orange packages. Less than a dollar each.
Those other models ( e-body for example ) have 90 degree insulated push on terminals. Those would be great to have/use here but... finding them for a #10 post in the aftermarket isn't easy. Majority are for #8 post, too small.