Could also be one of your valve lifters.  I remember in the past having to replace one as the spring got weak.

Thank you Dan. I don't drive it till it stops, so not too concerning, I did adjust the valves when this first started, but saw no change.

Maybe one or more of your valves is a wee bit out of adjustment and comes into spec as it warms up. If the tick goes away as the engine warms I don't think it is of much concern. Perhaps it is an oil pressure issue, occurring only when the engine has been sitting awhile and the oil has drained out of the passages and galleries. Once pressure comes up and they are filled, the tick is resolved. I doubt it is the mechanical fuel pump. If the cam follower is worn, the sound would last a lot longer.

I have tick, and the mini does too. On cold starts I have a ticking noise, sounds like a lifter in pitch, a tick per revolution, lasts about a minute, then goes away completely in just a few revolutions. If the car sits more than a week, the tick lasts longer. Restarts on the same day there is no tick. Oil pressure is about 60 PSI through the time it takes for the ticking to stop, and changes it rpm does not help it go away. The sound seems to be on the fan end of engine but hard to be sure. I run a mechanical pump, thinking possibly it's the problem, I see most replacements use a nylon tipped actuator arm. Thoughts? A+ 1275 1989

Thank you in advance.