I had envisioned a Kitsuki Investigator using Gao (tiger hook swords) to ensnare his opponents. I was planning to give her Ambidexterity for the re-roll, and Coiling Serpent Kata. But not sure since they’re being used in pairs, do I incur in penalties when I fight two handed?

ambidexterity, or, how to get reroll on every melee checks...

to answer your question, dual wielding gives no penalty and no bonus. some techniques/abilities supplement it though. but ultimately, unless you want to use a two handed weapon, no mechanical reason not to dual wield.

Thanks! I wasn’t sure, because I just couldn’t find anything...

As @Avatar111 says, there's no specific rules (good or bad) for 'dual wielding'.

• You can have a single-handed weapon in each hand (obviously this limits you to single-handed grips if a weapon has multiple grips).
• You can attack with either as a strike action.
• There is no default 'dual strike' action. Spinning Blades Style and the Mirumoto mastery ability Heart Of The Dragon let you roll from one strike action into a second.
• A Tinbe-Rochin pair lets you do a guard-and-strike combination as a movement & support action - increasing the TN to hit you by one and decreasing the TN of your next strike by one. Obviously that's your action, so it's an investment - either combine this weapon pairing with Air Stance for extra extra TN to be hit, or with Water Stance so you can fight from behind your shield each turn.
• Note that Ambidextrous wouldn't necessarily apply to every single roll - whilst you can argue for it, the benefit is about unexpected blows from your off-hand*, so whilst I'd probably let you get at least one reroll in a conflict scene, it's not going to be rerolls all day every day.

* "I know something you do not." "What?" "I.....am not left-handed."

15 minutes ago, Magnus Grendel said:

* "I know something you do not." "What?" "I.....am not left-handed."

There is something I ought to tell you.

... I'm not left handed either.