I might call the garrotte a small or medium grapple attack, innefective vs a target with rigid neck armor.
As per the rules, just adjust the grapple crit result so it always affects the neck vicinity as needed.
Keep in mind that if I were to toss a rope around your neck and start pulling, likely we'll end up bashing and flailing around, so it might not be totally out of line not to move damage to the neck if a crit reads "Breaks rib -20" it could easily mean that in the struggle to get the garrotte off, they broke the rib on a peice of furniture, a corner of the wall, the floor with the attacker falling on them, etc.
Grapple attacks progressively hamper the target. . .I'd likely also get into closed off air and blood flow in the form of progressive RRs after a few rounds of the neck grapple. (Then again, you could just treat the hits/crits as being partially due to the choking effect, with unconciouness coming at 0 hits).
IMO If the attacker gets a crit result with a % of grapple, then they have the garotte around the neck, if not, then the attack failed, and unless the target is severely hampered in movement I'd say it's time to switch weapons (I guess you could improvise jackie chan style and use the garrotte as nunchucks or try wrapping up their hand while fighting or something, but likely having blown it, it's time to run or just punch them.)
If the attacker did get a grapple %, I would then get into breaking the grapple for the target (per what Tim said above) and also allow further attacks by the attacker, continuing until the target is dead/breaks free, or the attacker decides to stop trying.
For a wide/soft garrotte, like a scarf, that would likely be it. . .for a thin/hard one like a rope or chain I might consider secondary krush criticals of lesser effect (Though the grapple table will crush things, so perhaps not). . .
with the wire slash crits may make sense. . . .but it's akin to the knife to the neck issue. . .a thin wire pulled by a heavy/strong person will quickly decapitate the target (and saw off fingers slipped into the garrotte at the same time) so it's almost akin to a "I walk up behind the guard and cut his throat". . .the wire is essentially a loop of knife edge. . . depends on how you, as GM would rule a PC slitting throats on unaware, but not helpless targets.