Who actually decides how working capital gets calculated on closing day?

Neither party unilaterally decides this on the day itself — the purchase agreement is supposed to define the methodology, the target figure, and the process in advance, so closing day is really just when that pre-agreed mechanism gets applied for the first time. Typically the seller prepares an estimated closing statement shortly before closing, based on an agreed accounting policy, and the purchase price at closing is adjusted using that estimate.

After closing, the buyer usually reviews the actual figures and prepares (or reviews) a final closing statement, and if the buyer and seller disagree about the final number, most agreements provide a defined dispute-resolution process, commonly referring the disagreement to an independent accountant whose determination on the accounting question is treated as final. The whole point of setting out this mechanism in detail during negotiation is to avoid an ad hoc argument on closing day itself about whose number controls. A buyer or seller who finds the agreement vague on this process should have it tightened up before signing, not after a dispute arises.