I typically find 3 to 5 years rust protection outside, maybe better in sheltered areas, and essentially indefinitely in the workshop. But it does wear off with handling.
Way I do it the surface does stay very slightly oily for a fair while. Not overtly so, more '"didn't think that was oily!" when you put it down and find the tiniest trace on your hands. Which may not be good in the kitchen.
Maybe spraying with WD40, as Hopper does, and carefully wiping off will leave a clean surface. Or perhaps try IsoPropanol alcohol.
That said I'm seriously slap dash about the whole process. Heat the bit up to blue(ish) and dunk it in the pint (ish) of oil I've had under the bench for so long I've forgotten what it is. Probably Castrol Magna BD 50 or Hyspin AWS 32 but it might be Shell Rotella. Maybe 15 years and counting methinks!
Gave up on old engine oil a long time ago as the results were too variable in colour and durability. Which I put down to all the additives and buts that make it multigrade. I recall getting all bad tempered when 5 parts came out about 8 different colours and grabbing the nearest bottle of straight oil for a do-over. 45 years or so back when I first started this old engine oil worked OK.
Clive