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Wrapped in a microfiber towel that I keep in one of my saddlebags. It seems I use mine all the time as others forgot to check their pressure etc so mine comes in handy.
My 11 Limited didn’t come with one but my little sister reminded me to get it when I picked my scooter up Feb 26th. I keep it in a bag I found at Wally World in the travel/suit case area. It is a bag (black) for toiletries and it holds the pump and tools with plenty of room for other maintenance stuff.
I think it's one of those things you don't really need on the bike all the time. If you're doing a solo ride and planning on picking up a passenger or vice versa than I could understand taking it but otherwise make your adjustments before you leave and good to go.
To you all who carry it with you, are your shocks prone to leaking? If not, then how often do you really need to change the pressure? I've got a simple mind, so please excuse my ignorance. I'm confident my shocks maintain pressure just fine, so checking is limited to maintenance days, and will stay that way until something out of the ordinary pops up.