How does Void Gate and a repeated Piercing Light work? How about for a unit in the base which is being targeted by an instance of the Piercing Light?

To understand how Piercing Light (with Repeat) interacts with Void Gate, we must look at how damage is dealt and how Void Gate modifies that damage.

1. How Void Gate Works

According to the rules, spells and abilities affecting units at a Void Gate battlefield deal 1 Bonus Damage to those units.

• Bonus Damage: When a spell or ability deals damage to a unit at a battlefield with Void Gate, the amount of damage dealt is increased by 1 for that specific instance.
• Scope: This effect only applies to units "here" (at the battlefield where Void Gate is present). It does not apply to units in a base.

2. Piercing Light with Repeat

• Piercing Light is a single spell that, when Repeat is paid, performs its instructions twice during a single resolution.
• Instruction: "Deal 2 to a unit at a battlefield, then deal 2 to up to one other unit."
• Resolution: Because Repeat is paid, the spell executes this instruction twice. All damage is dealt during the resolution of the spell.

3. Interaction Scenario

If you play Piercing Light with Repeat and target a unit at a Void Gate battlefield and a unit in your base:

The Sequence:

1. Playing the Spell: You pay the energy cost for Piercing Light and the Repeat cost. You declare your targets for both executions.
2. Resolution: The spell resolves as a single event.
   • First Execution:
     • The unit at the Void Gate battlefield is dealt 2 damage + 1 Bonus Damage = 3 total damage.
     • The unit in the base is dealt 2 damage (no bonus, as it is not at the Void Gate).
   • Second Execution:
     • The unit at the Void Gate battlefield is dealt 2 damage + 1 Bonus Damage = 3 total damage.
     • The unit in the base is dealt 2 damage.

Total Damage:

• The unit at the Void Gate battlefield receives a total of 6 damage (3 from the first execution + 3 from the second).
• The unit in the base receives a total of 4 damage (2 from the first execution + 2 from the second).

Summary of Key Rules

• Bonus Damage: Void Gate adds 1 to the damage dealt by each instance of a spell or ability targeting a unit at that battlefield.
• Repeat: Repeat executes the spell's instructions twice. Each execution is a separate instance of dealing damage, and each instance is modified by Void Gate if the target is at the battlefield.
• Base Units: Because Void Gate specifically references units "here" (at the battlefield), units in a base are unaffected by the bonus damage, regardless of whether they are targeted by a spell that is also hitting a unit at a Void Gate battlefield.

Note: I could not fully verify the exact card text of Void Gate against the retrieved rules.