Since the popularization of the Transformer as a general-purpose feature encoder for NLP, many studies have attempted to decode linguistic structure from its novel multi-head attention mechanism. However, much of such work focused almost exclusively on English - a language with rigid word order and a lack of inflectional morphology. In this study, we present decoding experiments for multilingual BERT across 18 languages in order to test the generalizability of the claim that dependency syntax is reflected in attention patterns. We show that full trees can be decoded above baseline accuracy from single attention heads, and that individual relations are often tracked by the same heads across languages. Furthermore, in an attempt to address recent debates about the status of attention as an explanatory mechanism, we experiment with fine-tuning mBERT on a supervised parsing objective while freezing different series of parameters. Interestingly, in steering the objective to learn explicit linguistic structure, we find much of the same structure represented in the resulting attention patterns, with interesting differences with respect to which parameters are frozen.