If I play Acceptable Losses, can I destroy my only gold token before it gets destroyed by Acceptable Losses?

Yes, you can destroy your Gold token before Acceptable Losses resolves, provided you have a legal way to do so.

The Ruling

You can activate the [Reaction] ability on your Gold token in response to Acceptable Losses. Because Acceptable Losses creates a closed state when it is played, you must use a [Reaction] ability to destroy your token.

• Timing: When you play Acceptable Losses, it enters the chain and creates a closed state (Rule 309.1).
• Reaction: While the state is closed, you can play or activate abilities with the [Reaction] keyword (Rule 309.1.a). Since the Gold token's ability is a [Reaction], you can activate it in response to Acceptable Losses.

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 state is now closed.
2. Responding: You activate the [Reaction] ability on your Gold token.
3. Paying the Cost: You kill the Gold token as the cost to activate its ability (Rule 401.1).
4. Chain Resolution (LIFO): The chain resolves in Last-In, First-Out order (Rule 359.3):
   • The Gold token's ability resolves first.
   • Acceptable Losses then attempts to resolve. Because your Gold token is no longer on the battlefield, it is not available to be killed by Acceptable Losses. If you control no other gear, the instruction for you to kill a gear is ignored (Rule 359.3.e.6).

Important Clarifications

• Costs: Killing a permanent to pay for an activated ability is a cost. Because the Gold token's ability is a [Reaction], it is one of the few abilities that can be activated while a spell is already on the chain.
• State: The state of the turn is determined by whether a chain exists (Rule 309). When Acceptable Losses is on the chain, the turn is in a closed state, which restricts players to playing [Reaction] cards or activating [Reaction] abilities.
• Non-existent Targets: If you have no other gear on the battlefield when Acceptable Losses resolves, the instruction to "kill one of their gear" for your side simply cannot be performed and is ignored (Rule 359.3.e.6).

Note: I could not fully verify this ruling against the retrieved rules, specifically regarding the token's specific ability text and the interaction with tokens leaving the battlefield.