The thing about reflowing the solder....
On the clusters I'm familiar with (various 70's B vans), those pins aren't soldered to the board. They're rivets of a sort. You must add the solder, which can change the leverage effect of the connector and cause the pins to flex a bit and start to peel up the copper from the board.
Also, the pins can get stuck in the connector and get pulled right off the board.
That round connector is the bane of my existence. I've always picked these vans up with bad instruments due usually to that voltage regulator, and there's usually only a handful of times one can connect or disconnect that round connector without damaging the board.
I've had to delete it entirely on my current van because half the pins were gone. I pulled the rest (careful! Don't peel up the copper) of the pins and put some little screw terminals so I can run u terminals to a generic molex connector.
Edit: here's this regulator upgrade to solid-state page, cheaper fix than that eBay http://1962to1965mopar.ornocar.org/ml-instrument-voltage-regulator64.html
Somewhere on the interwebs is a scan of an old magazine article detailing the same upgrade, but they used the shell of the old mechanical regulator to mount the transistor so it had stock appearance. I might could find it again.