  The dynamical assembly of binary black holes (BBHs) in dense star clusters
(SCs) is one of the most promising pathways for producing observable
gravitational wave (GW) sources, however several other formation scenarios
likely operate as well. One of the current outstanding questions is how these
different pathways may be distinguished apart. In this paper we suggest a new
multi-messenger observable that can be used to constrain the formation of BBH
mergers originating from SCs: the electromagnetic signal from tidal disruptions
(TDs) of stars by BBHs. Such TDs will show variability in their light curve
from the orbital motion of the disruptive BBHs, and can therefore be used to
map the BBH orbital period distribution, and thereby also the dynamical
mechanisms that eventually drive the BBHs to merger. Using an analytical
approach including General Relativistic effects, we find that the orbital
period distribution of BBHs within globular clusters peaks on timescales of
days, which we argue is unique to this assembly pathway. We propose that the
search for variable TDs in current and future EM transient surveys might be
used to constrain the merger history of BBHs in SCs.
