I'm just trying to desolder the existing joints at the moment.

Ah. They may have a clear plastic coating.

Your soldering iron looks fine (low-end, of course). Is the tip tightly
attached? Try loosening and retightening the screw while it is hot (use
care).

It's back in the packaging. Don't think swapping it for a 50W iron is
a
better idea? How about a flat tip instead of fine point?

30W is plenty for electronics; 15W would do.