Just thought I would mention that the originals had a counterbore depth of more than 5/8", as this style of starter pull knob also had a spring hidden inside.
I really should have used a vernier, it's approx 1 3/4" in depth. Of course this design is weaker as a result, hence they are sometimes damaged or missing. Note: the end of the spring has rusted away, it should close up where the cord knot is.
David