I too worry about the intrinsic quality. Is this one of those 'Napoleon's Hat' clocks? If it is the wheels and plates were never polished, they were as stamped out and never meant to be looked at.
Nearly 60 years ago I had a Saturday job in a clock shop and got the mucky jobs – cleaning clocks. For a Napoleon's Hat it was strip down, mark the going, striking and chiming wheels for identification and relative position. Then clean in 'benzine', dry off and brush with french chalk on a clock brush then peg out the holes. Rebush or hammer the holes as required. Clean out the spokes with a 3 corner graver, brush the wheels and reassemble.
For a nice Grandfather or carriage clock it was strip down, mark the going etc then polish all the bits with Brasso with a selection of really mucky crusty clock brushes and an electric polisher with a bristle wheel. Used to get covered in Brasso and black fingers. A cloth wheel and rouge for the plates and barrels except the front plate. Once all polished it was wash in benzine, re-do the grimy bits and rewash then dry off, french chalk etc.
Springs were anchored on a nail and cleaned with brasso while stretched out then benzined etc.
I was allowed to reassemble grandfather clocks but carriage clock bits were made perfect then put in tissue in a box and handed to No 2 Clockmaker who would moan like hell if any muck was found. All this for 10 bob and I hate the smell of Brasso to this day.
I have used the ammonia stuff and it is OK but does not seem to make the bits as bright. I hear some professionals make noises about 'preservation' as a cover for not doing too much. As it is quite easy to break a pivot etc I can understand. Also apprentices cost a bit more than 10 bob these days.
So have a good look, was it ever properly polished. That makes a big difference. BTW the 'benzine' was probably not really benzine but common or garden petrol, loads of it under the bench. Elf n Safety was not a big thing back then. TBH I think Fairy liquid and hot water would be OK and SWMBO's toothbrush.
One of those grandfathers was a big heavy job with latches holding the plates together. No 1 Clockmaker said – this was made by Tompion lad, be careful.