tabIndex on a perspective drop down causes strange focus behaviour

I've added a tabIndex to a perspective dropdown component. This component is tabbed to in the correct order but upon receiving focus this way pressing the up/down arrow keys don't cause the dropdown to open.

When rendered in the browser it seems that instead of using the <select> component the IA dropdowns are actually just various divs and labels and as far as I can tell the component that requires focus for the arrow key behaviour to work is the <div> with tabIndex=0 seen here:

I'm not sure if this is intended behaviour but it is causing me issues. I have an idea for a work around if anybody knows of a way to cause the dropdown to open through scripting? (I can add a onKeypress event to the parent div that is actually getting focus)

Alternatively does anybody know any other way around this issue?