This work investigates observations of gradual upward phase shifting of temperature oscillations in a steep tropical reservoir, which differ from the π radians sharp shifts that are usually accepted for the description of baroclinic motions in terms of normal modes. Supported on numerical modeling and theoretical inviscid wave ray tracing, we show that the gradual upward phase shifting is the signature of vertically propagating seiches, which refer to basin-scale oscillations that are stationary in the horizontal but propagate downwards in the vertical. We show that the vertically propagating seiche occurs due to the predominant supercritical reflection of the internal wave rays at the lake boundaries, which focuses the internal wave energy downwards with a minor fraction of the energy reflected upwards, resulting in a net downward energy propagation. The net downward energy flux precludes the formation of standing waves, with potential implications for the common framework of the energy flux path at the interior of stratified lakes. The analysis supports that vertically propagating seiches and standing mode preclusion are expected to occur in any given lake, but their signatures are more evident in steep sided lakes, with a wide metalimnion and/or for lower forcing frequencies, characteristic of higher order vertical modes.