Well I just pulled the pin. Definitely monkey’d with at some point. The grove looks nicely cut, and one end of the pin is crushed. Probably from previously being pulled in or out.
Measures to be a 2x10mm roll pin if anyone wants dimensions down the road. Slightly over on the 2mm for an interference fit.
Off to the hardware store to see if they have any…

Not sure where you are located but here in the U.S. Harbor Freight sells an assortment kit for $7.49, although the sizes are in S.A.E. sizes, I didn’t look but they might possibly have a metric kit as well. If you google “Harbor Freight roll pin” it will show a picture of the assortment box with the sizes that come in the assortment.

Good to know, I'm in the St. Louis, MO area (always down for a group ride in MTNF!). All the local hardware stores start at 3mm roll pins. There is a HF down the road from me, worth checking. Starting to look like a McMaster-Carr order to me...

Pin could be SAE...  some parts like steering head balls, check balls, and carb jet threads are not metric. 

The random pump i have which is probably early 360 has a pin measuring 2.08mm on the exposed part.
Could you tap a few turns of imperial thread into it to match a screw with an unthreaded stem for the cable ramp to run against. Na, maybe too hard.
Good if you can find a roll pin though.
The genuine hex head screw i've seen on some later pumps i recall,--or think--were stepped up in size from the miniature thread whatever thread it was.

A standard 5/64" pin before installation measures 0.083" to 0.086".  Nominal hole size is 0.078"

2.08 mm is about 0.082" 

Genuine part is likely best...  and possibly a mistake to assume it is "metric". 

Well I bought one of the 91608-20010 pins on Ebay so here are the pre installation measurements for anyone else in the future, looks like a hardware store SAE or Metric pin can work fine!

Dia (measured slit side to non-slit side): 1.95mm
Dia (measured non-slit side to non-slit side): 2.27mm
Dia (nominal): 2.11mm
Length: 10.31mm
Slit Width: 0.025" (feeler gauge)

That's good. So it went in tight & stopped before the shaft?. All working ok now?. Thanks.

Yep, just had to tap it in a bit, for sure be careful to not let it seat on the pump shaft! Adjusted pump and it seems to be working and oiling properly now.