Cycling from 500 to 1500 and back is (on the V12 and I suspect on the inline 6, others will confirm) a classic sign of an air leak into the inlet manifold.
Check manifold bolt tightness, throttle body and all vac tubes. Block off each tube, one at a time, where it enters the inlet manifold and see if it fixes the problem.
If it is any comfort, I am a great believer in replacing parts, assuming the car is a keeper. All new parts contribute to future reliability and prevent future failures!

 

There's a vac pipe attached underneath the 90 degree air intake elbow. This is prone to deterioration and coming loose.

Cheers

Paul

 

Thanks chaps. Unfortunately I've been unable to replicate the fault. I left the car stationary with the throttle held open at about 3000rpm for an hour to see if I could get the cycling behaviour to come back with the engine warm as before. No luck. I then took it for a drive, and it behaved flawlessly.

I neglected to mention that the cycling behaviour happened when I accidentally left the lights on and flattened the battery and had to get a jump start. I can't really think of a reason why that could have caused it, but for whatever reason I can't get it to come back now.

It seems like the misfiring issue has gone, though. Perhaps replacing the amplifier did solve it.