We examine the redistribution of energy between electronic and vibrational degrees of freedom that takes place between a π-conjugated oligomer, a phenylene-butadiynylene, and two identical boron-dipyrromethene (bodipy) end-caps using femtosecond transient absorption spectroscopy, single-molecule spectroscopy, and nonadiabatic excited-state molecular dynamics (NEXMD) modeling techniques. The molecular structure represents an excitonic seesaw in that the excitation energy on the oligomer backbone can migrate to either one end-cap or the other, but not to both. The NEXMD simulations closely reproduce the characteristic time scale for redistribution of electronic and vibrational energy of 2.2 ps and uncover the vibrational modes contributing to the intramolecular relaxation. The calculations indicate that the dihedral angle between the bodipy dye and the oligomer change upon excitation of the oligomer. Single-molecule experiments reveal a difference in photoluminescence lifetime of the bodipy dyes depending on whether they are excited by direct absorption or by redistribution of energy from the backbone. This difference in lifetime may be attributed to the difference in dihedral angle. The simulations also suggest that a strong coupling can occur between the two end-caps, giving rise to a reversible shuttling of excitation energy between them. Strong coupling should lead to a pronounced loss in polarization memory of the fluorescence since the oligomer backbone tends to be slightly distorted and the two bodipy transition dipoles have different orientations. A sensitive single-molecule technique is presented to test for such coupling. However, although redistribution of electronic and vibrational energy between the end-caps can occur, it appears to be unidirectional and irreversible, suggesting that an additional localization mechanism is at play which is, as yet, not fully accounted for in the simulations.