Identification of the subject of「目をそらすかと。。。」

Question

From what I understand, the expression 「〜のかと」 can be used to express the speaker thinking something might happen, as in 「〜のかと思って」. However in the below passage I am having trouble understanding what it means in context.

僕は、彼女の手のひらにも、汗がにじんでいるのを感じた。炎が、夜空の闇を照らしている。大切な文字が燃える、燃える。焦る。頬を汗が伝うのが分かった。ゆらぎ子が手を離さない。運転手を見た。目をそらすのかと彼女が手を握りしめたとき、その強さに、僕は諦めた。車は走り出した。

I think my biggest confusion here is who is the subject of 「目をそらす」. Is the speaker saying that she (彼女) gripped his hand tightly, as if she might look away? This doesn't seem to fit. Or is he saying that he was going to look away (from the taxi driver?) but then she gripped his hand tightly?

None of the interpretations seem to fit to me.

If someone can help me understand, I'd appreciate it.

Update: You can see this paragraph in context here.

Answer 1

So they have been looking at each other, right?

Then this 目をそらすのかと彼女が手を握りしめた implies she gripped his hand as if she were saying "Are you looking away from me? (i.e,. Don't look at the driver! Keep watching me!)" 僕は諦めた that follows would mean "so I gave up looking at the driver, and kept watching her."

If this still makes no sense, please provide a larger context.

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EDIT: Looks like my initial interpretation was wrong. Actually the protagonist was watching the "burning letters", and 彼女 gripped his hand as if she were saying "Are you looking away from the burning letters? (i.e., Stop it if you are thinking of something dangerous! All we can do now is to keep watching!)" And this 僕は諦めた seems to mean he gave up trying to go back and rescue the letters.