In the original pilot (The Cage), we see that Spock smiles:

As pointed out in the accepted answer to this question, the reason provided was that Spock was 'grinning with relief'.

It got me to thinking though; evidently at that stage of planning Spock wasn't entirely logical; he would still have emotional displays at time.

My question then is this: out of universe, when and why did the character of Spock become logical?