The brief
The Golf's gear changes had gone sloppy: a vague, loose feel at the lever, the gates not as defined as they used to be, sometimes a notchy or imprecise engagement. He brought it in. That's a worn shift linkage. The lever connects to the gearbox through a linkage of rods and bushings, and those bushings are nylon or rubber, so over the years they wear and develop play. Once there's slack in the linkage the lever movement doesn't translate cleanly to the gearbox, so the shift feels loose and the gates lose definition, and it can get worse until selecting a gear becomes a hunt. A worn linkage doesn't tighten back up, so the worn parts need replacing.
The diagnosis
A check confirmed it, the shift linkage had play in its bushings, the worn parts letting the lever move without the gearbox following cleanly, which is exactly the vague, sloppy feel. The gearbox and the clutch checked out, it was the linkage at fault. That's a linkage replacement, you renew the worn bushings and rods rather than trying to take up the slack, then adjust it so the gates line up.
The work
The worn shift linkage parts were removed and new genuine VW-spec components fitted, the bushings fresh, every fastener torqued to spec. The linkage was then adjusted so the lever sat right and the gates lined up cleanly, and the shift action checked through every gear. A road test confirmed a tight, precise shift, the gates well defined, and clean engagement through the box.
The outcome
A tight, precise gear change, well-defined gates, clean engagement, and the slop gone from the lever. The Golf went home shifting properly again. A worn linkage only gets sloppier until selecting a gear is a chore, so renewing the worn parts and adjusting it put the shift action back where it should be.