In the below sentence I translated the first part as "Men sometimes display" but cannot figure out the meaning of [これって脈アリサイン].
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これって”脈アリ”サイン ＝Might this be the "there-is-a-chance" sign?
When you want to find a hot spring or a valuable metals, you have to check 水脈 (the hot water pathway underground) or 鉱脈 (metalliferous vein) in advance.
脈がある means that there is such a 脈, which is something good, positive, and welcomed.
Now in the modern colloquial Japanese, "脈アリ" means that there is the possibility that the person likes you, has a positive feeling toward you, has a date with you, or becomes your lover.
[The sign of positive feeling toward you, maybe,] that men show you sometimes