Does Mask of Foresight choose a target when it gives the +1?

No, Mask of Foresight does not choose a target when it gives the +1 might bonus.

According to the card text, the ability reads: "When a friendly unit attacks or defends alone, give it +1 might this turn."

This ability does not use the word "target," and it does not meet the criteria for targeting defined in the Core Rules (Rule 355.10). Instead, it automatically applies the bonus to the specific unit that triggered the ability.

As confirmed by the RiftJudge FAQ (ID 6385):

• Mask of Foresight does not target.
• Because it does not target, it does not check for valid targets upon resolution.
• It "snapshots" the unit that triggered it at the moment the attack or defense is declared. It will grant the +1 might to that specific unit when the ability resolves, even if the battlefield state has changed (e.g., if other units have joined the showdown since the trigger occurred).