One Mysql Table with Multiple TIMESTAMP Columns
MySQL versions before 5.6.1 would not let two TIMESTAMP
columns in the same table, unless as you rightly noted with out defaults and allowing null.
MySQL 5.6.+ allows two or more TIMESTAMP
columns in a table.
More here: http://shankargopal.blogspot.in/2013/03/mysql-566-timestamp-columns-and-default.html
It's documented in the MySQL docs:
In addition, you can initialize or update any TIMESTAMP column to the current date and time by assigning it a NULL value, unless it has been defined with the NULL attribute to permit NULL values.
http://dev.mysql.com/doc/refman/5.0/en/timestamp-initialization.html