Life could be so easy: ride 10,000 miles, remove rear wheel to change tire, ride another 10,000 miles.
I guess Vespa doesn't want it to be so easy. Some only get 3-4K miles out of a rear tire. Mine started showing bald spots after about 4200, and from there I took it easier and got another 1000 out of it before I started getting worried. Today was the day (actually, last night was the night) where I finally got around to get that wheel off.
Did I mention Vespa didn't want it to be so easy? Instead of just removing the wheel, we have to remove the exhaust first, and then a plate, before we can get to the wheel. But I'm getting ahead of myself.
The tools I used:

L>R
Needlenose and flat pliers to deal with the cotter pin
3/8" ratchet & 17mm socket, 6mm hex wrench
6mm hex wrench
1/4" ratchet and 6mm hex bit
garden variety screw driver
side cutter
torx bit
(various removed bolts and parts)
a flash light
thick leather gloves
In the foreground:
1/2" x 25" breaker bar with short 24mm socket
extension pipe to extend hex wrench
The beginning (or the end):

Use a proper size torx bit to remove these three bolts, but, for now, leave the top right one (two red rings) in. It nicely balances the entire exhaust, even with the header undone.
Once the two bolts are removed and the top right is loose but still in, loosen the two bronze nuts at the exhaust header. This will eventually release the entire exhaust assembly and avoid issues with the exhaust gasket which the older GTS models have. I hear the newer GTS has a one-piece exhaust, so there is no other way.
To loosen these two bronze nuts, you will need a swivel or wobble extension for your 1/4" (preferred) or 3/8" ratchet, with a 10mm socket. You will need to lie under the scooter and fiddle until you got it in and working. A flash light will help. The good news is, removing these nuts is easier than later fitting them again. We'll get there in a bit.
Opening the battery cover will allow you to see both nuts and how you position the 10mm socket. Works both for removal and installation!
When you have loosened the two nuts, you will need to prepare for the oxygen probe to come off as well. To do that, continue from top. You'll have to cut the wire tie that holds the probe wire in its upper knee. Follow the wire continuing back down, and you'll see it ending in a flat plug. That plug is held in place by a rubber sleeve over a flat metal finger. Push it up from underneath the scooter with a screwdriver. Continuing from the top, undo the safety and separate the plug.
I'm not removing that cable anymore. Just cut that zip tie and then swivel the complete exhaust around that cable, by 180 degrees counter-clockwise, to park it under the scooter, out of the way.
Now you can go ahead and fully remove the two bronze nuts. Then, supporting the exhaust below the remaining torx bolt, remove that bolt, and the exhaust will come free. The protruding O2 probe and the header flange will sort of get stuck in the guts, so keep twisting and moving the exhaust to free it all without breaking off the sensor and then put the exhaust aside. It will look like this:

Notice that the oval retainer is loose and will slip down a bit from the pipe's end.
Going back to the plate, you will now remove the center nut over the axle:

First step is to remove the cotter pin. Straighten both of its legs and pull it out. I used needle nose pliers to grab it and then hit the pliers with a hammer to pull it out, after I had straightened it. Toss the old pin. Use a new one for reassembly.
Remove the safety cap. Now you have access to the 24mm center nut. I was forewarned that this nut would be the biggest challenge. So I went ahead and borrowed that 25" breaker bar, and with that, removing the nut was actually the easiest part of the whole procedure.

(In the white rectangle you can see the wobble extension with 10mm socket)
Okay. Remove the 24mm nut and the distance ring underneath.

Now you can take the next hurdle: removing the plate.

Go ahead and remove the 17mm nut over the shock absorber and pull the shock out from the bolt. Don't worry, you won't damage anything, just pull it out far enough so it comes free from the bolt. Move it over to the right of the bolt and leave it hanging there.
Remove the two 6mm hex bolts. My top one was a bit corroded inside, so it took some extra effort to get it loose. I needed that pipe extension over the hex wrench to extend my lever.
Once these bolts are removed, you need to pull off the plate. Be informed that it sits very tight over the axle. It worked for me to rotate the plate left and right while pulling, to slowly get it off the axle. Remember this when you later install it again, it will require a perfect alignment and the same kind of rocking/pushing to fit on.
Okay, now we finally get to what we really want: the wheel (this shows the new tire mounted already).

Remove the five 6mm hex bolts and take the wheel off.
Mark the rim with arrows ...

...for the installer to know how to mount the tire. In the case of a Zippy, also make sure they understand it is the rear tire. Motor bike service shops are usually not familiar with scooter wheels or GTS rims in particular, so let's give them some help to expedite their work and help to get it right the first time.
Back to the scooter: you now deserve a beer, while you stare at your scooter's naked rear end. I love naked rear ends...

Take the wheel and the new tire to a tire shop to swap tires and balance the wheel.
Once you're back from the tire shop, you simply get all the empty beer bottles out of the way and reverse the process. It took me 20 minutes (and this was the first time I did this) to install the wheel and the plate, and another 40 minutes (!) to install the exhaust...and I didn't have one single beer either. The 24mm spindle nut needs to be tightened with a torque wrench to 85-90 lbs/ft.
Here is what I learned about reinstalling the exhaust: a second person will be of help. I did it by myself, and here is how:
maneuver the header and probe end into the guts, aiming to seat the pipe into its hole in the cylinder head, while aligning the muffler's top right flange with its thread, and insert the torx bolt to hold the exhaust. It was extremely difficult for me to get that bolt in, due to my position under the scooter. For that step alone, a second person would be a trememdous help (for me, anyway).
I now use a 7 3/4" long 2x4 that I wedge under the exhaust at just the right spot (see picture). That positions the heavy exhaust just right to insert the bolt (in white eye) and align the header pipe on its two bolts.
Positioning the exhaust this way before you tighten the header pipe nuts has been proven to prevent tension and subsequent cracks in the exhaust--at least for me and for over 25,000 miles.

Next biatch is to get the bronze nuts back on. Without prior experience, I tried it in reverse order, and that doesn't work well. Here is how it will work the easiest: start with the left nut (left in direction of travel!). This nut is easier to install, you can do it directly with the ratchet extension. Don't tighten it yet, just go far enough to keep the oval retainer flat against the cylinder head.
The other nut is best threaded on with just the socket but without extension, and a 1/4" socket works better because it is slimmer. I almost got cramps in my hand, getting it done, and it took a long time until I finally had it, after so many trials-and-errors. Your mileage may vary, if you have a 1/4" wobble extension--I only had a 3/8" one, which is too thick to work for rethreading the nut. Again, peeping through the open battery cover will help tremendously in positioning the nuts.
Once the nuts are on, it is easy again. Tighten them equally but not too tight. Bronze is soft, and you can easily strip the thread.
Now plug the O2 sensor wire back together and take a class with Houdini to get the rubber sleeve back over its finger. Maybe you have someone with small, boneless hands nearby who could help you out with this, it may save you time and pain. I didn't bother securing it with a new wire tie--it doesn't appear to be necessary.
Hey, we're done! Check the tire pressure (mine was delivered with 18 psi!) and go for a ride after your BAC is back to normal.
Talking about tire pressure--I inflated to 32.5 before I went for a ride. It was a long ride. Like 80 miles. When I was back, and after everything had cooled down, the pressure was at 29. It may have been warmer when I first checked, it may have a slow leak. I need to check again.
⚠️ Last edited by windbreaker on UTC; edited 4 times