You are fairly limited here. The two common pattern/autocorrelation statistics appropriate for binary data are the "General Cross-Product Statistic" or the "Joint-Count Statistic". Unfortunately, these are not available in ArcGIS. Here is a nice introduction to these statistics: http://www.stat.ncsu.edu/people/fuentes/courses/madrid/lectures/areal2.pdf
There is a Bernoulli specification of the SaTScan statistic but it can be a bit tricky to implement correctly.
I have exactly the same problem only with discards of marine fish vs fish retained. I initiated the OHS but left out the overall distribution of all data points (0,1). Thank you for your excellent support on this issue.