The corks in the taps dry-out in storage - and leak.
Strip the tap, remove the cork and boil it in water (briefly). It will swell and become soft. It shouldn't leak after that.
Of course, if its been soaking in petrol for months I'm afraid there is a different problem
My avatar shows the late Len Rich in 1970 with the bike I now have - a 1958 Ariel VH