Are these the "eyes that seem to look for the only salvation"?
But in this case shouldn't it be 探す?
I'm confused, could someone help me please?
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見つけ出す is a compound verb which means "to find out" (focuses on the successful result of searching), while 探す is a simple verb which is closer to "to search" (focuses on the effort itself, regardless of the result). They are generally not interchangeable when talking about something in the past, but they can be interchangeable when talking about something in the future. For example, 敵を見つけ出すのが見張りの役目だ is almost the same as 敵を探すのが見張りの役目だ.
The phrase in question is definitely not something we use in daily life, so I don't know how to make sense of it without any context. But yes, it literally means "The eye which (seemingly) finds out the sole salvation."