This article shows the steps necessary to remove the headset cover on a GT or GTS. The pictures are slightly more confusing then they need to be due to the windscreen mounted on the shown GTS, and the nonlinear order in which I removed the parts of the windscreen.
Allen wrench, 2.5mm
Open-ended wrench, 17mm (or adjustable crescent wrench)
Screwdriver, Philips & Flathead
In this photo, you can see the uprights for the windscreen on my scooter. It would be best if you started off by removing the entire windscreen, uprights and all.
Using the 2.5mm allen (aka hex) wrench, remove the screws to the brake fluid reservoir covers.
Slide the reservoir covers up the mirror stem and hold them out of the way. Using the 17mm wrench (or adjustable crescent wrench, shown) loosen the mirrors.
Spin the mirrors out of their sockets and set them aside.
Using a flat screwdriver and a soft cloth, insert the screwdriver into the slot on the side of the Piaggio badge and gently push the handle of the screwdriver toward the legshield. Do not twist the screwdriver.
Unscrew the Philips-head screw that's behind the Piaggio badge.
With the headset turned to one side, lift the horn cover up and then toward you to remove.
For a GTS, disconnect the running light.
Remove the small screws (one each side) from below the outer edge of the headset, just below the brake levers on either side of the headset.
Remove the single screw from just below the headlight. Note that there are two screws here, but we are only interested in one of them. The lower screw holds the front of the headset cover in place, and should be black. The upper screw (which adjusts the headlight and should not be removed) is brass colored and is angled slightly. Warning: Do not drop this screw, or it will fall down between the glove box and the legshield and then probably down below the floorboards. In other words, you'll never see the screw again.
Grasp the front of the headset cover from below and carefully lift upwards to disconnect the internal tabs that hold the two halves of the headset together. You should see the top edge between the two halves separate from each other. Carefully move the front headset cover toward you, being careful not to snag the tabs on the brake reservoirs or anything else in the headset. This operation will require some careful flexing of the headset cover in order to clear all the various parts.
Disconnect the headlight connector from the back of the headlight.
Disconnect the pilot light connector.