Goodaltgamer: First you arrrre welcome.
They did remove the official linking for it, but it is still there, just a hidden feature. And in case as a general search tip:
Use your favourite browser and type:
site:www.gog.com gogdownloader.exe
first hit (at least for me).
What does it do?
It restricts the search to (here) www.gog.com, and just looking for the search-terms you enter afterwards.
Thanks Goodaltgamer. Fortunately I have the downloader downloaded. I was just worried that GOG might have "retired" the downloader when I wasn't able to log in, especially when I then searched for threads on the downloader to see if anyone else was having problems but just ended up with the GOG bear.
In hindsight I was just being needlessly paranoid and just needed to be a little more patient, especially in light of GOG's recent sale as their download servers were probably being hammered a fair bit.