As the concept of gap itself derives from comparison (one sequence is gapped in respect to another), I would say that in a pairwise alignment a gap will never occur in both sequences. In a MSA two sequences could be gapped in respect to a third one, but in this case you would not have a conceptual separation between query and subjects.
Generally, gaps like
don't have a biological meaning and are never reported by alignment programs (unless the result is a subset of a multi-species alignment) (or the program is broken)
More interesting are cases like this
which can be biologically meaningful although most alignment programs to not support them (transition from deletion-to-insertion state in HMM-speak)