These scenes are completely optional, but once you trigger all of them the two will marry. Raising heart levels and triggering scenes is the only way to get a rival couple married off.
To trigger Gill and Luna's 5 heart event, have 5 hearts with Luna (if you are female), or 5 hearts with Gill (if you are male). Walk out of your house in the morning, and Gill/Luna will be waiting for you. They want advice on their crush, and wonder if you can give them some encouragement. You can encourage them, or tell them it's a bad idea. To get the couple married off though, encouraging them is the best decision.
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Gill (ギル Giru) is a character in Harvest Moon: Animal Parade. He is one of the eligible...