[[WMG: Gordy caused Alternate to need a monocle.]]
In Alternate's flashbacks to his childhood, he didn't wear a monocle. However, when he was about a teenager to the age he is in the story, he's wearing one. Also according to one flashback, he and his father have been in mines for most of Alternate's life. In the third volume, we see Gordy has no problem with tossing his son around, throwing pick-axes at him, and even threatening to kill him.
Therefore, I'm thinking that sometime in Alternate's teenage years Gordy threw or hit him hard enough to damage his eye.
[[WMG: Alternate was only after the Eto Gun to make his father proud of him.]]
It's implied Alternate started pursuing the Eto Gun after finding a manual for it in Gordy's treasure chest, so he might have been trying to earn his father's approval.