Drupal - Where does drush look for the path of the mysql socket (on MAMP)?

First of all, check which php and php.ini file is used by drush:

$ drush status --full
 Site URI                        :  http://default                                                                                                          
 Database driver                 :  mysql                                                                                                                   
 Database hostname               :  localhost                                                                                                               
 Database username               :  root                                                                                                                    
 Database name                   :  drupal7                                                                                                                  
 Drupal bootstrap                :  Successful                                                                                                              
 Drupal user                     :                                                                                                                          
 PHP executable                  :  /usr/local/opt/php56/bin/php                                                                                            
 PHP configuration               :  /usr/local/etc/php/5.6/php.ini  

Then edit its default MySQL socket name for local db connects:

pdo_mysql.default_socket=/path/to/mysql.sock

as by default it points to /tmp/mysql.sock unless PHP was configured with different (--with-mysql-sock).

Check by:

$ php -i | grep ^pdo_mysql.default_socket
pdo_mysql.default_socket => /tmp/mysql.sock => /tmp/mysql.sock

So probably that's why /var/mysql/mysql.sock didn't work, as it was looking for /tmp/mysql.sock instead.

Then the symbolic link should work as expected.

If drush is using wrong instance of PHP, then add it into PATH (as you did) or specify with --php=</path/to/file>, so the right php.ini would be loaded.

Alternatively specify unix_socket in your settings file (as you already did).