For rotary switch care and cleaning - it always descends into a religious or holy war about what to do.
There is cleaning, lubricating and oxidation to deal with, 3 aspects. The different switch constructions matter greatly on how to do all that.
I found the ANENG multimeter rotary switches make poor connection, they are some slag filled copper on ENIG finish on the PCB. Ohms readings way up there.
Factory looked like a mineral oil film was there on the PCB.
I tried - polishing the copper, silicone dielectric grease and a few other chemicals, eventually the fix is applying PPE like (In North America) CAIG
DeoxIT F5 on the contacts/PCB.
The rotary switch works perfect for over 2 years now.
Clean it with IPA and q-tips. PAPER is a great abrasive to scrub off oxide without destroying and plating or surface finish. Anything coarser (sandpaper, scouring pad etc.) is destructive.
Fluke lube was mineral oil and I'll check but a light petroleum grease on the ratchet/shaft like Lubriplate.
Silicones are not preferred because they are like CFC's and can cause a contamination problem, I'd read parts near it can get affected.
WD40 is mostly kerosene and terrible, the solvent which attacks many things, evaporates and then you don't have decent lubrication. Some people love the stuff. ICK.