When a weakly bending rod consisting of discrete subunits is partially oriented in a weak electric field by an independent induced dipole mechanism, the off-field decay of its dichroism or birefringence reflects the same mutual-rotational correlation function that is manifested in its forward depolarized dynamic light scattering. An analytical theory of that mutual-rotational correlation function is developed by extending a previous theory for self-rotational correlation functions of subunits in macromolecules with mean local cylindrical symmetry, and the result is formulated in terms of a previous normal mode theory for discrete weakly bending rods. Results from this analytical theory are compared with those of Brownian dynamics simulations with generally good agreement. By dissecting the analytical theory, explanations are found both for the unexpectedly small fraction of total relaxing amplitude that appears in the rapid initial transient due to bending and for the absence of the relaxation time of the longest bending mode from that initial relaxation.