I've recently started hearing a noise I think from the engine. It happens when the car has set for anything more than five minutes. It is coming from low in the engine and sounds like a knocking. If I let it idle for a few minutes, I don't hear it on acceleration. Please don't tell me it's a rod.

 

With it starting after 5 minutes, (warming up) could it be a combination of the oil viscosity thining to much and worn main bearings? Reason I thought of this is that I had this happen to me back in the 80's on a Ford V8 motor, it would knock while idling, and quiet down when acccelerating. I changed the oil to a heavier blend, that stopped the knocking, but I still replaced the bearings soon after that.
On another note, I was in your neck of the woods a week ago on Friday, had to go to Jaguar of Tulsa to get some HSMO for my 88 XJ6.

Good Luck, Hope it is not anything serious.

 

Actually, at idle there is no knocking. It starts upon acceleration, but goes away after a few minutes of driving.

 

Engine knocks and noises can be indicative of so many things - some serious, some not so serious.
My advice to you is to go to someone really knowledge about your engine and let him listen; even an expert who has never dealt with Jag engines should do - these fellas have great ears - just make sure he's really well-recommended.