Human efficiency in finding a target in an image has attracted the attention of machine learning researchers, but what about when no target is there? Knowing how people search in the absence of a target, and when they stop, is important for Human-computer-interaction systems attempting to predict human gaze behavior in the wild. Here we report a rigorous evaluation of target-absent search behavior using the COCO-Search18 dataset to train state-of-the-art models. We focus on two specific aims. First, we characterize the presence of a target guidance signal in target-absent search behavior by comparing it to target-present guidance and free viewing. We do this by comparing how well a model trained on one type of fixation behavior (target-present, target-absent, free viewing) can predict behavior in either the same or different task. To compare target-absent search to free viewing behavior we created COCO-FreeView, a dataset of free-viewing fixations for the same images used in COCO-Search18. These comparisons revealed the existence of a target guidance signal in target-absent search, albeit one much less dominant compared to when a target actually appeared in an image, and that the target-absent guidance signal was similar to free viewing in that saliency and center bias were both weighted more than guidance from target features. Our second aim focused on the stopping criteria, a question intrinsic to target-absent search. Here we propose to train a foveated target detector whose target detection representation is sensitive to the relationship between distance from the fovea. Then combining the predicted target detection representation with other information such as fixation history and subject ID, our model outperforms the baselines in predicting when a person stops moving his attention during target-absent search.