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From the KZ440 manual, pg 235
"There is damping oil around the meter needle shaft which damps needle flutter and makes the needle move smoothly.  If the meters are left upside down or sideways for any length of time, the damping oil will spill out of the reservoir, and the meters will malfunction."

And that is all the manual has to say about the gauges, other than they can't be disassembled or repaired and must be entirely replaced.  Obviously, that's not going to stop me from trying.

Upon another inspection of what I believe is the damping oil reservoir, I do not see anywhere obvious that I could inject fluid.  If I could remove the needle, I could further disassemble the mechanism to figure out whats going on, but I'm still working on that.  Anyway, I have some things I can try from the above suggestions, so I'll let you all know what I come up with.

The oil reservoir has a a clear rubber cap. You can inject oil into it using a seringe. Use a light machine oil like 3 in 1.
If the damper has no oil in it the needle will fluctuate at little but the it will NOT be noisy like you described earlier. 
Not a khi guage but they are pretty much all the same. 

As I posted earlier, if it's noisy when on the bike but not with a drill then the cable very likely has a broken braid which is snagging as it rotates which will cause noise and needle flicker. 
 

wrote:

The oil reservoir has a a clear rubber cap. You can inject oil into it using a seringe. Use a light machine oil like 3 in 1.

 

Wow, that's very similar to my bike.  Thanks for posting!

Is the needle removable on that particular gauge? 

Also, is play that allows the metal cap to move back and forth ~ 1 mm with respect to the gauge face normal? 

Metal cap over the magnet drive shouldn't have any play. 
The needle on this guage has metal tangs that fold under the top bush. If you bend down the tangs the needle will come off. 
The head of the Bush the needle sits on is bigger than the hole in the clock face so the face can't be taken off without removing the bush. The bush is a tight push fit on the very fine central shaft. Unless you have to, don't try to remove the bush as it very very easy to snap the fine shaft and ruin the guage. 
If you do want to remove the bush then a couple of teaspoons, one each side under the bush  and gently lever both sides equally at the same time. AVOID levering so you are lifting one side more than the other or you WILL snap the shaft and wreck the guage. 

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If you do want to remove the bush then a couple of teaspoons, one each side under the bush  and gently lever both sides equally at the same time. AVOID levering so you are lifting one side more than the other or you WILL snap the shaft and wreck the guage. 
 

For tasks like this I've learned to pick up a spare item - preferably one that already doesn't work - and use it for practice. It's relatively cheap insurance.

For tasks like this I've learned to pick up a spare item - preferably one that already doesn't work - and use it for practice. It's relatively cheap insurance.

I really think I have to take the thing apart to find out what's going on with it.  Given previous comments in this thread and what I can see myself, getting a junk gauge to practice taking apart is the right course of action.  Where to get a cheap junker gauge is another question.  Cheapest one I can find on ebay is $25, which isn't terrible but hard to justify for a "practice" part. 

I used to live near this awesome Cycle Salvage in Baltimore.  Man I wish I had something like that around here in North Carolina (Raleigh area)!

Removing the needle - a common task for clockmakers. Here's what they use, or some variation of it: www.amazon.com/Jewellers-Tools-Remover-R...kmaker/dp/B017MPZVA4
Ian

So I just wanted to give an update on how the work went.  It turns out that the flicking needle and noise were not primarily a result of the gauge internals.  Rather, it was the drive mechanism on the gauge that the cable fits into.  Cleaning and oiling both of them stopped the noise!  I hope people read this before going through the process of opening their gauges.

I also learned that, at least for the tachometer, it is not possible to disassemble the mechanism past a certain point (at least not that I could figure out).  The only maintenance task that can be carried out is filling the needle damper canister with oil by a syringe.  Doing this seemed to help the tachometer needle stabilize somewhat, but probably not as much as just oiling the drive mechanism.

So thanks everyone and I hope that helps someone else out there.