Research funders around the world have implemented open access policies that require funded research to be made open access, usually by self-archiving, within 12 months of publication. Elsevier is unique among major science publishers because it produces several journals with non-compliant self-archiving embargoes of more than 12 months. We used Elsevier’s Scopus database to study the rate at which Australian and Canadian neuroscientists publish in Elsevier’s non-compliant (embargoes > 12 months) and compliant journals (embargoes ≤ 12 months). We also examined publications in immediate open access neuroscience journals that had the DOAJ Seal and neuroscience publications in open access mega-journals. We found that the implementation of Australian and Canadian funder open access policies in 2012/2013 and 2015 did not reduce the number of publications in non-compliant journals. Instead, scientific output in all publication types increased with the greatest growth in immediate open access journals. This data suggests that funder open access policies that are similar to the Australian and Canadian policies are likely to have little effect beyond an association with a general cultural trend towards open access.