You would be right in saying it's for the timer shutoff. Where to connect it would depend largely on how the system turns the engine off. The instructions for the alarm should tell you what part of the start/run circuit to connect into. "Engine extinguishing circuit" is pretty vauge. AFM vs MAP may also have a different system.
What you have to establish is what turns the engine off. You need to eliminate spark, air and fuel. You need to shut off the injectors and stop the spark. Something in your system controls this since it already happens when you turn the key off. Probably by removing power from a relay. So no fuel or spark means engine slows and if its AFM, when air flow stops, the flap closes and this triggers the fuel pump relay to open and stop pumping fuel. Also means that if you have an accident and the engine stalls that it won't pump fuel everywhere.
EDIT: After looking at the diagram more, you might be able to put another relay in the EFI Relay power supply line, using the shutoff wire to switch it on/off (again depends on what the wire does (power or earth)) This looks like it would cut power to the injectors and fuel system.
Not sure about what the last stages of a MAP engine are.
On the old site there in the tech section there is a listing for the AE86 book incl wiring as well as many others.
Also sideshow and mos on the forums are the considered wiring gurus.
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