A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
A player, 15 January 2014
Into the Wastes Engage: You have the first opportunity in this battle to pass or take a Battle action, which must come from a card in a unit.
Naval Engage: If you are the Attacker, you have the first opportunity to take a Battle action, which must come from a card in a Naval Personality’s unit. Passing that action does not count toward ending the action round.
If a player attacks with a personality that has Naval and the defender uses Into the Wastes what happens? Which of these effects has the priority?
A player, 16 January 2014
The effect that got played in the last place wins. If you announce and resolve Naval as your Engage action, and then your opponent uses Into the Wastes, Naval is overriden by ItW. If you then play eg Sneak Attack, Into the Wastes is overriden by Sneak Attack.
A player, 2 September 2015
viewtopic.php?f=59&t=106497&p=1403582&hilit=Into+the+Wastes+naval#p1403582
My question is why if the two engages creates an effect, the active player has to decide which resolves first.
Alex Jones (rules official), 3 September 2015
Into the Wastes Engage: You have the first opportunity in this battle to pass or take a Battle action, which must come from a card in a unit.
Naval Engage: If you are the Attacker, you have the first opportunity to take a Battle action, which must come from a card in a Naval Personality’s unit. Passing that action does not count toward ending the action round.
If a player attacks with a personality that has Naval and the defender uses Into the Wastes what happens? Which of these effects has the priority?
The rules under Timing Conflicts cover what happens when two or more effects are triggered simultaneously: these can be delayed effects, indefinite conditional effects or triggered traits.
However, Into the Wastes and Naval (and similar abilities such as Sneak Attack) don't create a delayed effect triggered by, say, the start of the Combat Segment: instead they create ongoing effects which change who gets the first opportunity to act in the action round. These are not covered by Timing Conflicts (as there isn't one), but instead by the text under Continuous effect conflicts: With two effects of equal specificity, the effect applied later overcomes the effect applied earlier.
You'll note, of course, that this section refers to "Continuous Effects", not "Continuous and Ongoing Effects" - I'll get this fixed.