In contrast to magnetic order formed by electrons' dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as "hidden order." Previously, the hidden order in phase II was identified as primary antiferroquadrupolar and field-induced octupolar order. Here, we present a combined experimental and theoretical investigation of collective excitations in phase II of CeB6. Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the low-energy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in a rotating field is calculated within a localized approach using the pseudospin representation for the Gamma(8) states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at a constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of intermultipolar interactions that stabilize hidden-order phases.