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I looked up the reading for `鏡` in `眼{め}鏡{がね}` on jisho.org
[here](http://jisho.org/search/%E9%8F%A1%20%23kanji), but I could not find
`がね`, only `かがみ`,`キョウ`, and `ケイ`.

Where did that reading come from?
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readings
Where did the reading for 鏡 in 眼鏡 come from?
「ガネ」 is not a reading for 鏡. The issue here is that the word 眼鏡 has a
[熟字訓]{じゅく・じ・くん}; that is, a reading applied to the entire word, not to the
individual parts. In fact, you can see 眼鏡 [at the top of this list
here](https://ja.wikipedia.org/wiki/%E7%86%9F%E5%AD%97%E8%A8%93#.E7.94.9F.E6.B4.BB.E7.94.A8.E5.93.81).

You can find many other examples of words with 熟字訓 on that same page.

In fact, even in writing your topic, you typed the word as 眼​{め}鏡​{がね} which
incorrectly associates the hiragana with the kanji. In cases of 熟字訓, I like to
enclose the whole reading in `« »`. So I would type it in as [眼鏡]​{«めがね»} and
it displays like so [眼鏡]{«めがね»}. But that's just my preference for how to do
it.
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To build on istrasci's answer, the がね is
[rendaku](https://en.wikipedia.org/wiki/Rendaku) for かね, with a basic meaning
of "metal" (and a more common kanji spelling of 金): "eye" + "metal" in
reference to the metal frame of eyeglasses. Modern glasses can use various
materials for the frame, but earlier, metal was the main (only?) material
used.
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