All resolved due to expert advice from Highway 61 and photomoof. Thanks, guys!
This problem was pretty obscure, but not unique to me, so I thought I would tell the whole story here.
I had to pull the top off my S3 to cure the unreliable flash operation. This is usually the fault of the contacts that live just behind the shutter speed dial, which tend to get wet from lubricants in the shutter setting mechanism, and then attract insulating crud. And the top is really easy to take off in this camera, right? Well, usually.
Here's the camera top. Remove the rewind knob and the plate beneath it, the shutter speed dial, the AR switch, and the ring underneath the wind lever assembly, and the top falls off in your hand. I have done this many a time with F's and a couple times with SP's, so I figured I was in for a one hour job.
Here's the wind lever. This usually just pops off with a bit of wiggling, or just undo the three screws holding it onto the brass bayonetting ring beneath it and the parts just lift off. However this camera used an earlier construction of the wind mechanism I had never seen before, and while the lever comes off with no problem, the ring beneath is is a quite different part from the usual design, and it is not immediately apparent how to get it off the camera.
Please note that it is not necessary to remove all the bits from the centre of the mechanism as shown in this picture. I had done so in my original disassembly because I was casting around for a method of taking it apart, and went hunting for hidden screws. In this design, there are three radial grub screws in the frame counter housing, visible through slots in the winder flange when the mechanism is in the standoff position from the camera body. Visible, that is, if the frame counter is rotated into the exactly correct position. Mine wan't, and so the screws were a mystery to me until "Highway 61" told me where to look for them.
With the screws removed or loosened, the frame counter housing and the winder flange can be lifted out, giving access to the last ring holding the top on.
This shows the removed housing, showing the location of one of the screw holes.
Here are top and bottom views of the winder flange.
So now the contacts are cleaned, the flash is working, and everything is back together, but it took a good deal more than an hour! I have never seen this construction in any Nikon repair manual, so I hope that this posting may be of assistance to the next person to encounter this unusual design.