Duct tape is not a standard onboard item. There is duct-type tape included in the security kit, but the security kit would not be opened in this situation. Many FAs (especially those that work the galley) carry a roll of masking tape with them. Pilots often carry tape as well, for situations like this.
It is not standard procedure for the cockpit crew to exit the cockpit to "fix" this type of situation (although it would have been nice if one of them took a look at it during a restroom break while they are out of the cockpit). While probably unnerving to the two passengers sitting at row 15, this situation does not represent a danger to the aircraft. The only time you would normally see them investigating something in the cockpit would possibly detrimental to the operation of the aircraft. For example, if FAs the detect a sound/smell that they can't identify, or sense smoke and can't determine the location or source, a cockpit crew member would probably come out to help identify the source so they could better troubleshoot the issue from the cockpit.