Thank you for replying.
Yes, I am trying to figure out exactly what kind of fitting it is. So that I can order the matching male threaded part with the concave recess that this hose connects to.
Since I asked on here, I asked on a marine diesel engine
group on Facebook. Very helpful folks there suggested that it's a BSP (British) hydraulic fitting. Which makes sense, since Perkins are from the UK. Photos of these fittings look right, so I am going to order these and see if the hose will connect to it. I am still looking for precise measurements of the shape of the recess for the cone, since we plan to head
from Fiji->NZ in a couple weeks, and with shipping
taking about a week each time, we can't have too many rounds of going "whoops, this one doesn't work" and having to try again.