LOL, they obviously didn’t want YOU to vote!
In my squadron, IIRC, our senior enlisted leadership were tasked with giving us the information, having us fill out the forms, and send them on their way. I don’t recall the mechanics, it was so long ago, but I do remember voting in the 1976 and 1978 elections that way.
You're right, they didn't. Nobody wanted me to vote. I had to wait 'til after my 21st birthday.