I'm trying to figure out in D&D 5e if an Artificer, choosing armorer and guardian, can add their intelligence modifier to attack and damage rolls with their off-hand gauntlet.
Each model includes a special weapon. When you attack with that weapon, you can add your Intelligence modifier to the attack and damage rolls.
Thunder Gauntlets
Each of the armor's gauntlets.
Would the off-hand gauntlet be considered a part of the special weapon mentioned in the first quote to gain the bonus?
Nowhere do the rules make a distinction between main hand and off hand.
Now, for the purposes of two weapon fighting, you cannot use the gauntlets to make a bonus action attack, as two weapon fighting requires each weapon to be a light melee weapon:
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
The gauntlets do not have the light property:
Each of the armor’s gauntlets counts as a simple melee weapon while you aren’t holding anything in it.
The “special weapon” of the Guardian Armorer is:
Each of the armor’s gauntlets
Each gauntlet is itself a weapon, and each gets the bonus from your intelligence modifier to attack and damage rolls.
Each model includes a special weapon. When you attack with that weapon, you can add your Intelligence modifier, instead of Strength or Dexterity, to the attack and damage rolls.
I know it says “weapon”, singular, and the guardian technically gets two, one for each hand.
unless you have Two Weapon Fighting style.
Thomas Markov is correct in that 5e does not distinguish between your main hand and your off hand so the ability to use intelligence for attack and damage rolls applies to both.
"Off-hand weapon" is often a reference to the weapon used for the bonus action attack granted by Two-Weapon Fighting. Thomas is correct that you usually cannot use Two-Weapon Fighting with your thunder gauntlets because they are not light weapons.
You can, however, use Two-Weapon Fighting with your gauntlets of you take the Dual Wielder feat which allows the use of non-light weapons.
You would not be able to add your Intelligence modifier to the damage of the bonus action attack granted by Two-Weapon Fighting.
The Armorer feature states:
you can add your Intelligence modifier, instead of Strength or Dexterity, to the attack and damage rolls.
Since you cannot add your Strength or Dexterity to the bonus action attack you also cannot substitute them with your Intelligence modifier.
