I'll again quote Caldwell's words here.
The Malayalam word for east, kizhakku, means beneath, and because melku (west) means above, Dr. Caldwell argues that the Malayalis must have come from the Tamil country east of the ghats, since there they had the low level of the ocean on the east and the high level of the ghat mountains on the west.
Other day, I was checking Tamil words for east and west. To my utter surprise Tamils also have the same words, kizh and mekku, for east and west.
Now, if Proto-Tamils became Malayalis then Tamils above ghats shouldn't have the same words. That in my opinion shows it's Proto-Malayalis who became Tamils(at least a section of them). This of course goes well with my old theory that Mangalore is the urheimat of SD-I speakers. The diversity of SD-I languages along Mangalore-Nilgiri belt in fact shows SD-I speakers first moved along coastal Karnataka region then migrated inwards.
Directions in Dravidian languages:
In my opinion, the directions in Dravidian languages need to be studied properly. Only in SD-I there are independent words for north and south common to most of the languages in the branch. For east and west all the words appear to be local innovations after languages became independent. However, it is clear that none of these were part of Proto-Dravidian or Proto-Dravidians were directionless people.
The words for north and south, baDagu and teGku, are common to Kannada, Tamil, Tulu and Malayalam. The words for east and west are mUDu and paDu respectively in Kannada(Tulu). However, Malayalam word for east is 'kilakku' and west is, though Caldwell/Logan call it 'melku', at present 'padinjayir' which cognates with Kannada 'padu' is in the common usage.
Kannada east and west are directly connected to sun's movement where 'mudu' means 'form' or 'rise' and 'padu' means 'fall', 'die' or 'set'. In fact, Malayalam west 'padinjayir' means 'setting sun'(padu + njayir (sun, nesara in Kannada)).