Revision B --
If the noise is heard only with a cold engine and during deceleration my first and primary suspect is the Air Injection System.
Do force the noise as described earlier and see if it matches what you are hearing. Given the situation you describe I strongly suspect the noise is from the AIS being active and we just have a failure to communicate how the noise sounds. If the noise is definitely not the same then read on...
There are a few rare '05 engines that experience premature valve guide wear due to excessively tight stem seals starving the guides of lubrication. This noise will almost always start at the upper left (clutch) side of the engine. The only sure check, per Yamaha, is to pull the exhaust header and look for oil residue. Your FJR will continue to run fine and will always get you home. Over
tens of thousands of miles it will gradually get worse and oil consumption will start to go up. This is not a panic problem like the CCT.
There is one other thing that can cause this kind of noise but I didn't want to panic anyone. Many Gen I engines have an inadequate Cam Chain Tensioner (CCT) which does not have the strength to take out all the cam chain play resulting in a rattling noise heard at the right side timing cover. If you have a rattling noise in this area you need to have the CCT replaced ASAP. There is a new CCT design, identified by a blue dot and this should be the only CCT that you can buy. There have been some engines that have suffered catastrophic cylinder head damage due to the CCT so don't take this noise lightly. If the cam chain is rattling the CCT has failed because as long as the CCT is good you will not hear the rattling noise.
Please do yourself a favor and either you or your shop listen and confirm where the noise is coming from if it is not the AIS. You can use a real mechanic's stethoscope to listen to the timing cover and the exhaust header for noise or 'make' one of you own. You can use a long screwdriver or better, any long metal rod then with a fully warm and idling engine put the rod on the timing cover then put your ear to the rod. You will be amazed at what you can hear. Next, go to the left side of the engine and then through the faring openings, press the rod on a header tube and listen for a noise described as silverware being rattled in a drawer. In this Forum the noise is called The Tick or Ticking -- do a search there are even sound clips of the noise.
I really hope the noise you hear is the the AIS, followed by The Tick. Best luck!
Edit: Corrected a massive amount of typing and formatting errors