My guess is that the system was originally base 5, because of the dual form for 8, implying that the finger-counting form for 8 was symmetrical - possibly with the four fingers bent over tips to the palm, or implying repetition of the same sequence of movements again (with possibly the thumb marking that the sequence was repeating). Later perhaps it became base 12 - moving the thumb across the inside of all the knuckles. [Including the tips of the fingers in that sequence allows 16 (0 - F), but that doesn't seem relevant here].
I suspect the the different logic different finger-counting systems is also behind the variants δεκαδύο/δώδεκα, δεκαέξ/ἑκκαίδεκα, δεκαοκτώ/ὀκτωκαίδεκα, δεκαπέντε/πεντεκαίδεκα, etc., but haven't got a clue where to go with testing or developing that idea
