I own a dozen centrepins and fish with them all. I have re-profiled pins and end-play adjustment screws to salvage worn out reels and I'm perfectly happy with good old 3 in 1 Oil for them.
I use cotton buds to clean the hole through the spool and I 'change 'the oil a couple of times a season.
To 'run in' a newly bought or repaired reel, I simply sit and spin it in my lap whilst watching the TV and then give it an oil change.
You can certainly try sewing machine oil or gun oil, if you wish, which are thinner, it's true, but my Speedia spins for 3 minutes on 3 in 1 Oil...that's smooth enough, surely?
Mostly it's about getting the reel to start spinning easily, with little or no effort, and that comes from light spool weight and polished components .... a long spin time is irrelevant, really, but people always like to see it...me included[:I]