To know how to approach it we first need to know whether things like Extra Attack or Compartmentalized Mind (No Mental Separation) function like Always On abilities or Transient "free action" ones.
P153's guidelines take some time for me to puzzle through...
I think maybe it doesn't fit the 2nd requirement of an Always-On ability? The "built-in discrete uses" part: you do have discrete uses of attacks, and once you use them up, you need to wait until your next turn for it to recharge and give your more uses, right?
Which should mean that it's functionally transient as a free action?
The underlying advantage basically has "a duration the user can't control" (1 second or less) because a finite duration is specified? That being 1 second, at which point it will be the next turn and you use another free action to reactivate it?
You could buy "Extended Duration x10" as a +40% enhancement. This means you only need to use 1 free action instead of 10 free actions to get 10 seconds worth of Extra Attack.
That's largely pointless (free actions are free) unless it were tweaked to take longer than a free action to activate Extra Attack, like for example if you wanted to limit it with "Takes Extra Time".
You'd need several levels of that to make up the cost of Extended Duration though... like for example here's a couple ways to save 2 points by netting -10%:
(Takes Extra Time 3 -30% Extended Duration 3x +20%) take 4 ready maneuvers to prep, then you get 3 seconds worth of +1 attack
(Takes Extra Time 5 -50% Extended Duration 10x +40%) take 15 readies to prep, then you get 10 seconds worth of +1 attack
(Takes Extra Time 7 -70% Extended Duration 30x +60%) take a minute of readies to prep, then you get 30 seconds worth of +1 attack)
(Takes Extra Time 9 -90% Extended Duration 100x +80%) take 4m of readies to prep, then you get 100 seconds (1m40s) worth of +1 attack)
(Takes Extra Time 11 -110% Extended Duration 300x +100%) take 15ms of readies to prep, get 300 seconds (5 minutes) of +1 attack
TET 13 -130 / ED 1000x +120 = 1h of readies get 1000s (16m40s) of +1 attack
TET 15 -150 / ED 3000x +140 = 8h of readies get 50m of +1 attack
TET 17 -170 / ED 10,000x +160 = 30h (1d6h) get 10,000s (166m40s or 2h46m40s) of +1 attack
and so on... seems pretty balanced. It only becomes a problem if you allow Permanent at +300% and the GM could always opt to just disallow permanent and follow existing patterns (30 million x duration at +300%, 100 million x duration at +320%, etc)
TET increases activation time by x32 per -40% while ED increases duration by x10 per +40% so it becomes progressively worse the more you pair this. It's great if you can schedule lots of prep time before a known battle but otherwise is bad because you're very inflexible about when you can fight.
Aftermath: TET (-5% per level) is one idea to shift that (activate as a free action, but you're forced to pay the readies when duration expires) but I don't think Aftermath should be allowed on abilities with durations longer than 12 hours. That's when Maximum Duration ceases to give you points, and getting Aftermath on an ability w/ Maximum Duration: 100 years (-0%) while technically legal in PU8p11 terms, is an abusive point crock.
Sort of like spending 50 points on this:
High Pain Threshold [10]
HP+4 [8]
Regeneration (Extreme, Costs 4 Hit Points per second -80%) [32]
Half the cost of Regeneration (Very Fast) [100] and netting double the HP per second :)
We gotta be wary of how we apply time/HP/FP based limitations on advantages (or enhancements to advantages) which give us extra time/HP/FP
Maybe that's why only Limited Use and Trigger (1 m intervals) was initially specified for Aftermath? Max Duration wasn't actually mentioned until the Expanded Aftermath example of Insubstantiality.
I don't know if we have a term for a mitigator (limitation which makes disadvantages cheaper) as applied to limitations.
We do have "Not Limitation is an Enhancement" precedent in Fantasy (F130 "Behind the Curtain" pricing +40% for "not having Divided Magery") which is how Either/Or Limitations are designed (Restructurable Magery being one such) but I don't know if that could help here...
I don't think you actually bother with giving Maximum Duration to transient abilities though, only stuff which is infinite duration by default.