The problem is, beast does not have the native capacity to get the correct light balance for sustained Time extension chests. Honestly, only red mage, blue mage and a fully skilled pup can do that.
Kill speed combined with ruby lights (open azure chests) will do the trick for BST. You're obviously not going to build lights as fast as jobs who can get native Azure kills, but it can work. Magic kills aren't the only way to build Azure lights.

The problem is, beast does not have the native capacity to get the correct light balance for sustained Time extension chests. Honestly, only red mage, blue mage and a fully skilled pup can do that.
Also BLM. For the reasons mentioned above. Except you want to be opening every Ruby chest with pearl instead of Azure.