I don’t believe you’ll be able to hear the injectors click on a running engine (except a Roll Royce, perhaps). A hydraulic tappet might click when engine is started some hours after being stopped, but the clicking disappears as soon as oil pressure is build up inside the tappet.
If the tapping noise is from the top end of the engine, it can be a number of faults. A clicking could be a tappet against the cam if the hardening of either has gone. If this is the case better change the offending item soon as it will ruin the other.
We all know what’s wrong if it’s a beginning diesel knock – the infamous cam variator. On late cars (engine No. higher that 144000) it can be repaired, otherwise it need at some time be renewed but won’t break.
If the noise is deeper it could be a piston or piston-pin connecting to the conrod. This will be easiest to hear on a cold engine at idling shortly after starting, disappearing (nearly) when hot. This, too, need attending to soon as a broken piston or conrod will ruin at least the cylinder – in worst case the engine entirely.
I agree that 0W-40 (Mobil F1 oil) is a bit thin (for summer use) but my 2,0 16v ran the first 60k miles on F1 with no apparent ill effects. A 10W-40 (or 50/60) is much better suited as an all-year oil (the viscosity 50/60 only keeps the oil from going too thin then really hot). However, I don’t thing thicker oil will make the tapping/clicking go away. I hoped that (my variator made the diesel knock when started hot) but it didn’t make any difference.
Good luck tracking down the cause of your noise.