If you've never done any soldering before, I suggest you practice on an old junk board before taking to your Mac Plus board. It's very easy to apply too much heat for too long and end up cooking the copper tracks off the board.

One of the pins on that connector looks like it has been really hot. In this situation, it can be really hard to get the fresh solder to "take" to the pin. I suggest removing the connector from the board and cleaning that pin up with some fine emery paper, or if you have Dremel tool, the wire brush attachment on the Dremel tool. Make sure that the fresh solder flows evenly across the copper trace on the board and the pin and properly wets the joint. If you just blob the solder on, you'll be back to where you are now in no time.