If I use Acceptable Losses to kill a Gold Gear token, can I still tap the Gold Gear to get power, or would I then have to pick a different Gear to destroy to resolve the spell?

Yes, you can use the Gold gear token's ability in response to Acceptable Losses, but it will affect how Acceptable Losses resolves.

The Sequence

1. Playing the Spell: You play Acceptable Losses (an [Action] spell) while the game is in an open state. It enters the chain. The game state is now closed.
2. Responding: You activate the [Reaction] ability on your Gold gear token to gain its power.
3. Paying the Cost: As a cost to activate its ability, you kill the Gold gear token (Rule 401.1).
4. Chain Resolution (LIFO): The chain resolves in Last-In, First-Out order (Rule 359.3):
   • Gold Gear Ability: The Gold gear's ability resolves, and you gain its power.
   • Acceptable Losses: Acceptable Losses attempts to resolve.

Impact on Acceptable Losses

When Acceptable Losses resolves, its instruction is: "Each player kills one of their gear."

• Because you killed your Gold gear token to pay the activation cost of its ability, it is no longer on the battlefield when Acceptable Losses resolves.
• If you have no other gear on the battlefield, the instruction for you to kill a gear simply cannot be performed and is ignored (Rule 359.3.e.6).
• You do not get to pick a different gear if you had no other gear to choose from initially; you simply fulfill the instruction as much as possible (which, in this case, is nothing).

Important Clarification:

• Costs vs. Effects: Killing the Gold gear is a cost paid to activate its ability, not an effect of the ability. Once it is killed to pay for that cost, it is in the trash and cannot be used again.
• No Targeting: As established in RiftJudge FAQ #4344, Acceptable Losses does not target. Players choose their own gear to kill at resolution. By destroying your own gear in response, you effectively prevent Acceptable Losses from being able to kill that specific gear.