Do both sentences sound natural?
1) I took a chance and approached the girl I had been interested in at the last minute.

2) I gambled on approaching the girl I had been interested in at the last minute.

Question

Do both sentences sound natural?
1) I took a chance and approached the girl I had been interested in at the last minute.

2) I gambled on approaching the girl I had been interested in at the last minute.

Answer

Yes but you would need to use punctuation in your sentences otherwise it means that you were only interested in her at the last minute ;-)
So - I took a chance, and approached the  girl I had been interested in, at the last minute

Answer

In everyday speech, number 1 is most natural.  You could also rearrange the sentence.
At the last minute, I took a chance and approached the girl I had been interested in.

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