Ah yeah, definitely at least a couple of those pins aren’t connected at the base of the pads.
While some will not reccommend this, I will in this case. If you have an old conical style tip, or if you threw one in the bin earlier
then you can pull it out, and take it to a bit of sand paper and fashion it into a (T12) BCM2 style tip, i find this shape particulary good at tight connectors and because of the large tip area it has enough thermal mass to give a good joint, I’d typically use this style if i have to resolder a pin on the LCD connector for example as my usal goto D24 is of such a shape that it can’t properly transfer the heat in these cases.
I mean it won’t be as good as a store bought tip and it will lose whatever coating was originally present but it should do the job… and lets face it, there’s no other good use for conicial tips 
I think it’s a good skill to learn, and you’ll appreciate it later on down the line, especially when you don’t have any of those entire connectors in stock