Okay, I lost my directions completely in my previous post. Tamils and Malayalis sharing east/west in fact do not contradict Caldwell's words. I should be careful not into fall in the trap set by imaginative people.
Anyway, I would consider it as Tamil superstrate influence on Malayalam. The Malayalam common word for the west is paDiJAyir (that is a cognate with other SD languages like Kannada/Tulu/Tamil and Telugu). I would rather think Malayalis would have kept kizhakku/melku pair in common usage had they been the people who coined them. But what has happened to the word denoting the east that would have made a pair with the west? Curiously, Kannada/Tulu, Telugu and Tamil don't have a cognate for the term east. May be the word was highly variable and probably had multiple terms based on the sun.
It appears Kodava and Kota words for the east is 'ki', same as Tamil/Malayalam. Both tribes are traditionally highland,western ghat, people for whom eastern region (Tamil) is beneath. That may show Proto-Tamils' migration route to present day Tamil region from present day coastal Karnataka region.