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Murdoch, even when attached to a Mercenary Unit, is a Trencher.

Finn's special ability, Desperate Pace, allows him to target a Trencher unit with a speed buff.

What's the rules interaction here? Can Finn even use Desperate Pace on Murdoch, and, if so, does it affect only him, or the entire unit?

There is no rule interaction, even though Murdoch is a Trencher, the unit that he attaches to is not and doesn't become one, and Finn's special ability will only target Trencher units, not Trencher models.