WFM. (Works For Me.). Current version of Firefox (63.0.3 (64-bit)). It was slow - took maybe 20 seconds after the first click to do more than cause its icon to flicker between black and red - but then it worked.

For those that are having difficulty installing the current version: Accessing the Firefox-extension-page for this add-on from another browser (Safari) allows access to the previous version page, but that new URL address needs to be copied back to Firefox before it can be downloaded. Here's the link:
https://addons.mozilla.org/en-GB/firefox/addon/openaccessbutton/versions/?page=1#version-1.6.1-signed.1-signed

Firefox keeps saying the file is corrupt. I even attempted to download it from the Open Access Button website, but it just led me back here. I'm using Windows 8.1, Firefox 47.0.1