Tip looks a bit oxidized except for the very end which on these pointy tips have a hard time accepting solder. Tip tinner works well for these issues.
Here is how to use it for best results.
You iron's tip looks oxidized and is likely not transferring heat well because of the oxidation buildup. You need to make sure to tin your iron's tip, that's putting solder on the tip when you're not using it and especially keeping a layer of solder over it when you shut the iron down. I would try and use a brass/copper sponge and clean the tip in that while trying to apply solder to it. You can also buy something like this to clean the tip:
Worst case scenario is you might need to just buy a new tip and make sure to keep it tinned regularly.
There’s also a product called Tip Tinner that coats and replenishes the tip. After prolonged soldering sessions or after every third or fourth normal uses, I use it and find it keeps my tips in good shape for a long time. I like to shut off the iron, then immediately clean it quickly in the brass mesh, wipe it on a sponge, soak it in solder, shake off the excess solder, then dip it in the tinner and let it cool off.
Soldering iron, solder (60/40, make sure it says rosin core), audio jack of choice (1/8", 1/4", mini xlr), wire (I recommend replacing the wires connecting driver to audio input. Working with the original wires was a massive headache for me. Any shielded copper wire works, pre-tinned makes it super easy to work with). You also need something to file down the hole where the wire was, either a file or dremel tool or even rough sandpaper. Try to find a jack that snaps in like this and covers the hole at the same time. I think that covers it
Though you only have 6 total points to solder, some things that will make it a lot easier are solder tinner (like this) and solder tip cleaner (like this).