Reading this is certainly interesting ...

Bromptons are simple, just have a particular way of setting up.

9/10times the issue is poor set up.

The 3 speed is 99% of the time a breeze to set and forget. If you are having issues its not set up properly.

If the bike shop does not deal Bromptons or doesnt seem sure DO NOT TRUST THEM.

I think I read something about older parts etc. The age of the mechanic does not depict their knowledge, do not be shallow. I am 23 and can strip a Brompton back to a bare frame and rebuild , just like I could a 1950 Pashley or a 2018 Sram Etap roadie!

The image posted by Jur is perfect. If the end of the smooth barrel is lined up with the end of the axle 99% of the problems I see are solved. Further than that the internals are worn/broken but this is very uncommon being honest.

In the last year I have serviced over 250 Bromptons including over 50 BSR / BWR hub services. - again, 99% of problems with the 3 speed are solved by the tension on the toggle chain.