Trench Run states:

"You may engage the Death Star dial as though it were a dark side objective (it is not an objective)."

Since it is not an objective, it seems that the only way to damage the Death Star dial with Trench Run is through engagements. Cards such as Rebel Assault (which can damage objectives) cannot be used on it. Is this correct? If so, it's a little disappointing that the cards in the objective set don't synergize very well with Trench Run.

Also, what about Target of Opportunity? That says "deal 1 damage to the engaged objective"? Is the Death Star dial temporarily considered an objective during an engagement? Or do you ignore that effect too?

You are correct. The dial can be engaged as an objective, but it is not an objective for the purposes of card effects that target and/or interact with objectives (you couldn't capture to it, for example), or for LS Balance.

However, I would agree that it qualifies as an "engaged objective" while it is engaged. Otherwise, Blast Damage wouldn't apply during strikes.

Ktom, are you gonna be a rules master for this game as well?

"Rules Master" is an unofficial thing. At this point, I've just happened to play a game or two with Trench Run.

And does the reaction of Wookiee Navigator work with Trench Run ?

Yes, Wookiee Nav allows you to engage the DS dial (via Trench Run) a second time. "Engagement" is the key word - as a rule of thumb, anything that refers to engaging an objective (eg Wookiee Nav), or to effects on an engaged objective (eg fate cards), count. Anything which simply refers to an objective (eg Rebel Assault) wouldn't.

Trench Run is a beautifully thematic card - but obviously hard to word perfectly and tightly without a few questions.