We study the problem of determining the emergent behaviors that are possible given a functionally heterogeneous swarm of robots with limited capabilities. Prior work has considered behavior search for homogeneous swarms and proposed the use of novelty search over either a hand-specified or learned behavior space followed by clustering to return a taxonomy of emergent behaviors to the user. In this paper, we seek to better understand the role of novelty search and the efficacy of using clustering to discover novel emergent behaviors. Through a large set of experiments and ablations, we analyze the effect of representations, evolutionary search, and various clustering methods in the search for novel behaviors in a heterogeneous swarm. Our results indicate that prior methods fail to discover many interesting behaviors and that an iterative human-in-the-loop discovery process discovers more behaviors than random search, swarm chemistry, and automated behavior discovery. The combined discoveries of our experiments uncover 23 emergent behaviors, 18 of which are novel discoveries. To the best of our knowledge, these are the first known emergent behaviors for heterogeneous swarms of computation-free agents. Videos, code, and appendix are available at the project website: https://sites.google.com/view/heterogeneous-bd-methods