Modern search engine result pages (SERPs) become increasingly complex with heterogeneous information aggregated from various sources. In many cases, these SERPs also display results in the right rail besides the traditional left-rail result lists, which change the linear result list to a non-linear panel and might influence user search behavior patterns. While user behavior on the traditional ranked result list has been well studied in existing works, it still lacks a thorough investigation of the effects caused by the right-rail results, especially on complex SERPs. To shed light on this research question, we conducted a user study, which collected participants’ eye movements, detailed interaction behavioral logs, and feedback information. Based on the collected data, we analyze the influence of right-rail results on users’ examination patterns, search behavior, perceived workload, and satisfaction. We further construct a user model to predict users’ examination behavior on non-linear SERPs. Our work contributes to understanding the effects of the right-rail results on users’ interaction patterns, benefiting other related research, such as the evaluation and UI optimization of search systems.