Transformer-based language models have shown an excellent ability to effectively capture and utilize contextual information. Although various analysis techniques have been used to quantify and trace the contribution of single contextual cues to a target task such as subject-verb agreement or coreference resolution, scenarios in which multiple relevant cues are available in the context remain underexplored. In this paper, we investigate how language models handle gender agreement when multiple gender cue words are present, each capable of independently disambiguating a target gender pronoun. We analyze two widely used Transformer-based models: BERT, an encoder-based, and GPT-2, a decoder-based model. Our analysis employs two complementary approaches: context mixing analysis, which tracks information flow within the model, and a variant of activation patching, which measures the impact of cues on the model's prediction. We find that BERT tends to prioritize the first cue in the context to form both the target word representations and the model's prediction, while GPT-2 relies more on the final cue. Our findings reveal striking differences in how encoder-based and decoder-based models prioritize and use contextual information for their predictions.