Good Morning, new member here, but have been on other sites. I am not as grouchy as I may appear.
From heraldry, the eagle should face to its right, called Dexter, towards the sword arm. Facing it left is called Sinister and gets into a whole lot of rules concerning coats of arms, But I digress a bit.
From the 1900 Revenue cutter service uniform regs, the first mention of an eagle as part of the rating badge is mentioned. Borrowed from the USN, the eagle faced to its left. The rating badge was worn on either sleeve, depending on which watch you were assigned to.
By the time the CG was established in 1915, the USN established the system of right and left arm ratings. The CG adopted all ratings to be worn on the right arm.
After the Pay Act of 1920 that made CG ratings and USN ratings the same. The CG shifted to right arm, seaman branch ratings and left arm ratings, engineer and artificer and special branch ratings.
In 1940, the rating badge was changed so that both right and left faced forward, symbolizing ready to face the enemy,
Bit long winded for a first post. I kind of took up a hobby of being able to trace the lineage all CG ratings and uniforms back to about 1829..