When I clean the minerals out of a showerhead, I’ll leave it in a bag of vinegar overnight or 8 hours over the day and agitate the bag every few hours(just a shake or two).

I don’t really have it down to an exact science, I just use vinegar to clean non-precious metals and plastics because I know white vinegar dissolves dirt and grime well enough and dries without a smell.

Since the vinegar is going to get inside the wheel around the axles, I would probably dry them in white rice afterward after shaking off as much vinegar as possible, since you can do the same thing, just leave it in a bag of white rice overnight, the white rice draws out moisture really well.

Otherwise, I feel like some of the vinegar will still be trapped between the axle and plastic casing for a pretty long time and could poorly interact with any lubricant you spray in there.