sorry to tell you this scott... but yer gonna have to put it down:( ill take it off your hands if you like... heehehehehee;)
id say a sticky lifter at cold start up... or, and much worse, a collapsed lifter thats on its way out. depends on the tap-tap-tap noise though. sounds weird, but ive run a litre of ATF through the engine oil for a day or two of driving, then change your oil and filter. give it a shot. cant really hurt. or find an engine additive that cleans all the crud out and change the oil. if its a bad lifter then the head comes off. and if you do that, may-as-well get a thumpy cam and new lifter;)
my 2 cents...
My feeling on engine flush / cleaning products & other magic elixers is , yes they will tend to loosen and release some of the gum and sludge that accumulates within a high milage engine BUT , in doing so can induce an oil consumption issue by removing the varnish n' such from the ring lands. What happens is clearances are now to the point where blowby can now get by the rings more easily , the deposits that were there are now gone. Use good quality oil , change it regularily to minimize deposits. I've disassembled & rebuilt lots of engines , the difference between an engine that has been maintained and fed quality lubricants and one that has been neglected or serviced at random with low grade lubricants is quite dramatic.
The opportunity to do proper servicing often is , I believe , the responsibilty of the owner from the point of sale when a vehicle is new and usually beyond the control of an owner who has purchased a high milage , poorly maintained vehicle , the damage has already taken place.
Additives & fancy oil enhancers , I feel , are for the most part snake oil , some work , some don't , I don't buy them so can't really offer an evaluation on what is the best to use.
Scott , you have a lifter that bleeds down when parked , not a big deal , it goes away on it's own.