I'm currently in Morocco and there's no way my tool kit will fit under the seat. It's in a Kriega US-10 bag in my panniers which, if I dump the panniers, can be strapped to the rear carrier.
You're going to need tyre levers, spare front and rear inner tubes and so on. Here's my listing
US-10 tail pack
rachet and extension
torx, allen keys, sockets
wrenches fixed, adjustable
screwdrivers--various
long nose mole grips
spare nuts and bolts
electrical wire and terminals
insulation tape
lighter, duct tape
Rapid Steel putty (mend holes in engine)
spare ear plugs
workshop gloves thin + heavy duty (change tyres)
bike manual
French/Spanish biking vocabulary
head torch (in case it's dark)
scalpel or sharp knife
spare rok straps, spare Zumo mount, spare Gerbing (heated jacket) cables
electric tyre pump with pressure gauge
tyre levers (one with 24mm spanner on end)
chain cleaner, chain brush
chain lube, WD-40
multimeter
Start with a Kriega or similar tool roll (£17), add most of the contents of the Halfords Professional 1/4 socket set (£15 when on special offer), stubby spanners from Maplin (probably £12), and you are half way there.
This trip I'm on my F650GS twin and to the amazement of the garage attendent, mended a puncture in my front tyre in five minutes flat. One big plus point of tubeless tyres. With the F800GS that's a good half hour job.
If you wear glasses take fixed focus reading ones (not bifocal or varifocal) in case you need to work on the bike. And they shouldn't be reactolite either.