Solved. This will automatically unregister on the death of the actor when the Magic Effect dispels.

It is amazing what you forget after 6 months.

Scriptname CInvisibility extends ActiveMagicEffect  

SPELL Property Invisibility Auto 

Event OnEffectStart(Actor akTarget, Actor akCaster)
    RegisterForAnimationEvent(GetTargetActor(), "weaponSwing") 
    RegisterForAnimationEvent(GetTargetActor(), "arrowRelease") 
    RegisterForAnimationEvent(GetTargetActor(), "weaponDraw") 
   RegisterForAnimationEvent(GetTargetActor(), "MRh_SpellFire_Event") 
    RegisterForAnimationEvent(GetTargetActor(), "MLh_SpellFire_Event") 

endEvent
 
 
Event OnAnimationEvent(ObjectReference akSource, string asEventName)
 	if (akSource == GetTargetActor()) 
  If (asEventName ==  "weaponSwing") || (asEventName ==  "arrowRelease") || (asEventName == "weaponDraw") || (asEventName ==  "MLh_SpellFire_Event") || (asEventName ==  "MRh_SpellFire_Event")    
Utility.Wait(0.3)
   		Invisibility.Cast(GetTargetActor(),GetTargetActor())
 	EndIf
EndIf
endEvent

No Death Dispel: If checked, the effect persists even if the target dies.

That suggests if it's checked, constant effect abilities with scripts keep on trucking long after death. I'm not sure how to test that though. Magic effects are so tricky :/. You could unregister it through OnDying(it's faster than OnDeath) to be on the safe side.