(1)
 
use Keyword Item Distributor (KID) to add a keyword to potions like this:

Keyword = Pickpocket_TimeIncrease_7|Potion|FortifySkillPickpocket03

use KID to add a keyword to effects like this:

Keyword = Pickpocket_TimeIncrease_7|Magic Effect|0x802~StealingNotBrowsing.esp

(2)

use a script on your effect to edit the properties of the main StealingNotBrowsing script

Important:

do not add the keyword to potions that have a 0 duration effect cause it will not work.
here's why:

if akBaseObject.HasKeyword(Pickpocket_TimeIncrease_10)            
            AddMagicEffectToPotion(akBaseObject as Potion, StyyPickpocketPotionEffect, 1, 0, (akBaseObject as Potion).GetNthEffectDuration(0), 0, none)
            PotionTimer = 10.0
endif
and
if (PlayerRef.HasMagicEffectWithKeyword(StyyPickpocketTimerKeyword))
        result += PotionTimer
endif

as you can see, the way this works is by dynamically adding a increased timer effect to potions with the correct keyword. It gets the duration of the keyword effect by looking at the duration of the FIRST effect of the item. If that first effect has a duration of 0, the timer won't be increased