Do both the buyer and seller have to sign the section 167 election form when a business is sold?

Yes. The section 167 election is a joint election, which means both the purchaser and the vendor have to complete and sign the prescribed election form together, it isn't something either party can make unilaterally or that automatically applies just because the deal happens to qualify. Both parties are agreeing, jointly, to treat the transaction as one where no GST/HST is charged on the transferred business assets.

This matters because if only one side signs, or the form isn't properly completed by both, the election isn't valid, and the sale can end up being treated as fully taxable after all, exposing the purchaser to an unexpected HST bill and the vendor to a potential obligation to have collected tax that wasn't charged. It's also generally the purchaser who needs to be a GST/HST registrant for the election to apply, so the vendor's participation alone isn't enough even with a signed form.

Because the election is only as good as both parties' cooperation and the accuracy of what's signed, this should be built into the closing documents and confirmed by both sides' advisors as part of the transaction, rather than treated as paperwork to be sorted out afterward.