  Bulk dislocation lattice defects are instrumental in identifying
translationally active topological insulators (TATIs), featuring band inversion
at a finite momentum (${\bf K}_{\rm inv}$). As such, TATIs host robust gapless
modes around the dislocation core, when the associated Burgers vector ${\bf b}$
satisfies ${\bf K}_{\rm inv} \cdot {\bf b}=\pi$ (modulo $2 \pi$). From the time
evolution of appropriate density matrices, we show that when a TATI via a real
time ramp enters into a trivial or translationally inert topological insulating
phase, devoid of gapless dislocation modes, the signatures of the preramp
defect modes survive for a long time. More intriguingly, as the system ramps
into a TATI phase from any translationally inert insulator, signature of the
dislocation mode dynamically builds up near its core, which is prominent for
slow ramps. We exemplify these generic outcomes for two-dimensional
time-reversal symmetry breaking insulators. Proposed dynamic responses at the
dislocation core can be experimentally observed in quantum crystals, optical
lattices and metamaterials with time a tunable band gap.
