Does a personal guarantee get released once the vendor take-back note is fully paid off?

Generally yes in substance, since a guarantee that specifically secures a particular vendor take-back note has nothing left to secure once that note has been paid in full, but this should be confirmed formally rather than simply assumed once the last payment is made. Whether the guarantee is actually limited to that specific note, or is drafted more broadly to cover "all present and future obligations" the buyer may owe the seller, makes a real difference here, since a broadly worded guarantee would not necessarily end just because one particular debt is paid off.

Because guarantees can outlive the specific debt they were originally given for if worded broadly enough, a buyer who has paid off a vendor take-back note in full should proactively request a written release or discharge from the seller confirming the guarantee is at an end, rather than relying on the underlying debt simply being gone. Keeping that written confirmation on file protects the buyer if a dispute or misunderstanding arises later about whether the guarantee is still technically in force.