Category fluency is a widely studied cognitive phenomenon, yet two conflicting accounts have been proposed as the underlying retrieval mechanism -- an optimal foraging process deliberately searching through memory (Hills et al., 2012) and a random walk sampling from a semantic network (Abbott et al., 2015). Evidence for both accounts has centered around predicting human patch switches, where both existing models of category fluency produce paradoxically identical results. We begin by peeling back the assumptions made by existing models, namely that each named example only depends on the previous example, by (i) adding an additional bias to model the category transition probability directly and (ii) relying on a large language model to predict based on the entire existing sequence. Then, we present evidence towards resolving the disagreement between each account of foraging by reformulating models as sequence generators. To evaluate, we compare generated category fluency runs to a bank of human-written sequences by proposing a metric based on n-gram overlap. We find category switch predictors do not necessarily produce human-like sequences, in fact the additional biases used by the Hills et al. (2012) model are required to improve generation quality, which are later improved by our category modification. Even generating exclusively with an LLM requires an additional global cue to trigger the patch switching behavior during production. Further tests on only the search process on top of the semantic network highlight the importance of deterministic search to replicate human behavior.