Consider that a gedan posture, and indeed a seigan kamae, have the hands and hilt of the sword fixed to or near the navel. The navel is considered the seat of the mind in traditional Japanese thought, and of course is the general location of the seika tanden (seika - below the navel). Thus, while we physically see with our eyes (nikugan, flesh eyes), we see/perceive intuitively with our seigan (true eye, or alternatively "pure eye" with the kanji that Ueshiba uses).
Incidentally, there is no reference to "the enemy" in the original doka.
下段をば Gedan wo ba
陽の心を You no kokoro wo
陰に見て Kage ni mite or In ni mite
打突く剣を Uchizuku ken wo
清眼と知れ Seigan to shire
I'd translate the last part simply as "Know the striking, thrusting sword (or the sword that strikes and cuts) as seigan." In context it could very easily apply to your own cutting and thrusting blade.