I took that tool kit out from under the seat and put it in one of the KQR panniers where I can get at it easier, along with a few other important tools. Normally I have a tail bag in place, so it's hard to get the rear seat on and off. On longer trips, I tie on a waterproof bag of personal gear using the grab rails.I took my seats off and noticed that big bulky pouch of tools under the rear seat and was wandering if the majority of owners remove them, looks like they about get in the way of mounting the rear seat
Now that I can post pictures...I was able to upgrade my tool kit with a small folding ratchet, socket drive hex in all usual sizes, and sockets for just about everything on the bike. Then I was able to move it to the empty space between the rear seat and the battery compartment. I did the mod that removes the round head screws that mount the front seat and used socket heads as posts instead, so now the front is seat removal is tool free.
I found a cool small Cordura pouch that fits where the original toolkit was. I've added quite a few aux tools, tire repair stuff with CO2 Filler, emergency cash, a small leatherman multi tool, removable blade screwdrivers, and a lot more. It has a couple of small outside pouches that I've made good use of.
I was also able to store 10! CO2 bottles in a padded bag on top of and beside my factory battery, and still have room for a rolled up microfiber towel to pour tools out onto.
I'm impressed with how much I've gotten under the seats with creative placement. I've never owned a bike with more room.
Mine is a 2015 with Kawi Gel seat, I know your mileage may very.