We were out for a ride yesterday in our “new” F-Type P300 and noticed a tick-tick-tick noise behind the drivers seat, at idle. It seemed to increase in frequency with the revs, but went away much above 2,000 rpm’s, or, with the ambient noise, maybe we could just no longer hear it.
Is this normal? I’m guessing it’s the fuel pump, but then, I just sold a 1973 Triumph TR6 and bought this modern beauty. It’s a different world for me.

 

It's hard to identify the source of noises in those cabins... There is an engine 'tick' at startup, but on my car, it goes away after warmup. But I have a plain ol' F... other P300 owners will probably have more suggestions.

 

I don't have a P300 (2.0 litre inline 4 cylinder turbo) but I suspect you are right and it is the fuel pump.
All the F-Type engines including the four potter are direct injection and use (very) high pressure fuel injection and they all have noisy high pressure fuel pumps to some degree.