While the PCI DSS doesn't specifically call out holding on to a customer's card, it's covered by 9.6, "Physically secure all media." To quote the testing procedures,
9.6 Verify that procedures for protecting cardholder data include controls for physically securing all media (including but not limited to computers, removable electronic media, paper receipts, paper reports, and faxes).
The card itself is a physical media containing cardholder data - think of it as someone faxing you a copy of the card, only without the paper :). "Physically securing" would mean some sort of access control to ensure that only authorized personnel (e.g., staff) and not unauthorized personnel (e.g., barflies reaching over the bar) can get to it. Inside a register drawer might work well, because that's something that's got due diligence protection since it's protecting your cash anyway, and all your staff has necessary access without added disruption.
The card might actually different in that it contains the CVV, which cannot be "stored" as per PCI DSS 3.2.2. But since cards are physically handed to staff constantly (e.g. your waiter takes it to the back to swipe it), obviously that's handled differently with physical transactions. I'm afraid I don't have any insight on the nuances there.
Which leads me to my summary... PCI DSS advice you get here
- may be biased towards Card-Not-Present (CNP) transactions, and
- PCI DSS advice is only an opinion unless it comes from a QSA.
I would encourage you to think of this as one of those times you need to pay a certified auditor to guide your implementation. (And I think that @AndyMac's suggestion about authorizing some amount and then settling for the full tab amount later is probably the right way to go, although I have no idea how signature is finessed in that situation if the customer leaves without signing - my experience is biased towards CNP transactions.)