Can you recycle a gold gear for the BF sigil of the storm?

No, you cannot recycle a Gold Gear to satisfy the requirement for Sigil of the Storm.

According to the card text of Sigil of the Storm, when you conquer the battlefield, you must "recycle one of your runes."

As established in the game rules and FAQs:

• Rule 403.1.b states that "Runes are Recycled to the Rune Deck."
• A "Gold Gear" is a Token (as noted in the FAQ regarding the Legion keyword), not a Rune.
• Because the effect specifically requires you to recycle a rune, you cannot substitute a Gear, a unit, or any other card type to pay that cost.

If you have no runes to recycle, the effect will trigger and resolve, but it will simply do nothing, as you cannot fulfill the requirement.