PiNimukam is a synonym for Peacock (ChoodamaNi nigandu – 3-50) and not elephant.
It came to be associated with Vinayaka as 'aagu-peyar' of peacock.
The puranaanuru urai (the urai is by an unknown author, written in an undated past and recorded in palm leafs and brought to print by Dr U.Ve.Sa) that I quoted from Dr-U.Ve.Sa's 'Puranaanuru moolamum, uraiyum' 1950 edition, says that PiNimukam or the peacock was carried in the flag in war fronts to remove all obstacles. Since piNimukam was considered as Pillaiyar himself taking control of the obstacles, Pillaiyar himself was called as piNimukam. The verse from Kalladam-7 indicates this.
But then there was an elephant used by pillaiyar as his vehicle. This is mentioned by the urai asiriyar who says that it used to be said that this elephant was known as piNimukam.
Thus we have two versions, one authenticated in texts (as peacock and Pillaiyar's peacock 'piNimuka magjjai' – kalladam -7) and another mentioned by texts as elephant due to popular usage.
The name piNimukam to the elephant seems to be an acquired one due to its association with Pillaiyar.