There are two white connectors side by side, and the blue connector next to them. The blue is the GPS antenna (as you know) and the white connectors are mated to a single connector with two leads coming out of it on the factory install. So you have a twin and a single antenna connection in reality. The blue one is all okay, and the white one has only a single connector going to one side, and you have a spare brown wire, yes?
I don't have this brown wire on my Jetta, but I've a feeling you might have to buy an adaptor to get it to connect on to the head unit. Obviously the RNS510 has been retrofitted, and someone "forgot" to do it properly. Mine was factory fitted so it's done proper like.