This paper presents the design of a thermoacoustically unstable combustor experiment for identifiability. We examine the impact of sensor placement, flame location, and acoustic excitation frequency on the Fisher identifiability of a one-dimensional combustion stability model's parameters. The model uses linear delay differential equations to describe both the acoustics and heat release dynamics in a laboratory combustor called a Rijke tube. We derive analytic expressions for the frequency-domain Fisher identifiability of the model's parameters. This leads to two key insights. First, excitation frequency, flame location, and sensor placement all have a significant impact on parameter identifiability. Second, the optimal excitation frequencies for identifiability are not strong functions of sensor placement but change with flame location. Building on these insights, the paper concludes by using a genetic algorithm to optimize the design of a Rijke tube experiment for thermoacoustic model identifiability.