Years ago I received a broken speedometer from Brant, thinking at the time that I'd use its parts to repair mine. I opened that one by prying the ring and that worked out pretty good. But at the time, mine started acting okay and I boxed up the mishmash of parts for another day.
I finally decided today was the day to open the thing up and fix it. And I didn't want to cut the ring and then try to figure out the best way to seal it back up. Here's how I did it.
Opening a GL1100 Speedometer or Tachometer
This is similar on all analog gauges.
On the GL1100 speedometer (and tach, I assume), there's a small cutout in the back case's lip. Back being the one toward the front of the bike ... with the cable mount and wires sticking out. (Oh man, now I'm confusing myself.

If your ring is clean all the way around, that cutout is as good a place to start as any. If your ring is discolored or rusty that's where you want to work. You'll be prying up about half the way 'round and then you'll hide that area down and to the inside.
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I have a large collection of dental tools in the toolbox. They are very strong and have various tip shapes. Pretty handy things that I picked up at a swap meet for cheap. You might use a utility knife (careful) or a pocket knife for this step.
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Work your tool back and forth to open a small gap.
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Just pry the ring up enough to be able to slip in a small screwdriver.
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With the screwdriver just catching the tip, press in and then down on the handle. Do not twist the screwdriver, you'll make major dents and may even tear the ring. Work the ring up a bit and move the screwdriver 1/16 inch sideways. Then press in and down on the handle a bit. Do that for 1/2 inch or so and then work back over the same area lifting the edge of the ring a little more.
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Continue the in and down action until you lifted half way around the ring. Take your time, take a break, smoke 'em if you got 'em.
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When half of the ring has been bent up you're ready to pop that baby out. At the half way point of your bent-up area, slip your screwdriver under the ring and over the case -AND- the rubber sealing ring. Try not to gouge into the rubber.
Lift the screwdriver up this time and the rear case should start slipping out from under the ring. But don't push up so hard that you bend the ring any more than it already is. You might have to move around and pry up in your bent-up area. Be patient and it'll come free.
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Remove the two Phillips head screws.
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Open up the wire ties.
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Separate the case. The ring will stay on the front case (the one with the glass).
The GL1100 trip meter knob will slip through the hole in the case, but you will have to tear the boot away. Mine was already torn away so I didn't worry about it much. I just glued it back in when reassembling. I've seen notes about some Honda speedos that say the knob is reverse threaded. Turn it clockwise to remove it. I tried holding the stem with needlenose pliers and turning the knob but it would not come free ... your results may vary.
If you got it apart okay, putting it back together is a breeze. Put the gauge into the front case and thread the wires back through their holes in the back case.
Thread the two Phillips screws in but do not tighten them down.
Slip the un-crimped section of the ring back over the back case. This takes a bit of doin' but you'll get it on there. Tighten the Phillips screws. Center the trip shaft in its hole.
For the next step, I picked my biggest (and oldest) pair of pliers to put the ring back on. To protect the ring from scratches, cover the tips of the pliers with duct tape, cloth or something. I used masking tape which wasn't quite up to the job so I had to watch it and replace as needed.
With the bottom jaw of the pliers, press in and up on the ring on the front case. Then gently roll up the bent-up part of the ring. You don't want to clamp the pliers down, you want to roll the edge of the ring in. Start at one end of the bent part and work around, gradually moving the edge back into its place.
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Opening my case took about an hour and closing it up took about half an hour.
Now, put it back on the bike and go for a ride already!
(I swapped parts from two speedos and did a little light lubing with White Lithium Grease while I was in there. On the broken one, I tried to remove the needle to see how I'd put on new faces, not that I needed them but just to experiment. I broke off the needle, don't know how you'd get it off or how you'd get it back on in the correct position. If replacing the face, I'd cut a slit or two in the middle and slip it over the needle, then just glue those cuts down.)