If a scope gap is discovered after construction and the work has already begun, documentation is absolutely required before the trade commences. Document the scope gap, check to see if it has already been allocated to another task, and then issue a Request for Information (RFI) to define the source and assigned responsibility of the gap.
Field discovered gaps put intense time pressure on the team to issue a verbal instruction to continue work, and deal with the necessary paperwork to legitimize the work later. Avoid these types of verbal agreements. Before any work is undertaken, ensure the cost and responsibility are agreed to by way of a contract variation, a potential contract variation, or a variation to the agreed scope.
The resolution of the gap should be formal, and follow the normal change management process. A field level agreement should not be used. Retain the RFI and the response to the RFI in the documentation in the event the scope gap is challenged in the future.