I think they are an amphenol type pin and socket connector
system. I have a Black Line pack, but have yet to burn out a
socket to look carefully and need to fix one.  The back end of
each pin in such a connector has a half cup that you set the pre
tinned conductor in, heat the cup side, and add solder to the
open side of the cup.  Similar connectors with smaller pins for
multi channel dimmer control in theatrical stage dimmers, and
larger connectors for the power outputs to multiconductor cables
from those same dimmers. I have soldered a lot of them.  Re-
using a pre soldered connector requires a lot of solder sucking
braid and a gas torch and lots of flicking the heated connector
to dislodge old solder before you can think about using it
again. The big power ones I have worked on are over $120 each,
so yes, you reuse them.  Be methodical. Start from the back side
to the connector, towards the middle, doing the edges as you go.
The biggest one I have soldered had 28 or so pins. It just takes
time and patience