Possible manifestations of a linear isomer of a rare gas-halogen molecule van der Waals complex in its B <-- X excitation spectrum are analyzed using a continuous one-parametric family of X-state potential energy surfaces (PESs) with variable depths of minima in the T-shaped and linear configurations. For the HeBr2 complex as an example, the propensities in the frequencies and intensities of the representative transitions from T-shaped and linear isomers are analyzed and the variation of the whole spectrum with the topology of the X-state PES is established. Qualitatively good agreement with the experimental HeBr2 spectrum clearly suggests that the unassigned secondary band of the observed spectrum is likely formed by transitions from the linear isomer, whose energy is very close to that of the T-shaped one. Present results provide strong evidence for the possibility to detect a linear isomer of rare gas-halogen molecule complexes via conventional excitation spectroscopy.