I've been able to review first posts and late posts for a while now - and it's actually kind of fun. However, there usually aren't any review tasks available (at least on SO), presumably because others also think reviewing is fun.
So, I would propose that a number be shown next to the review button in the toolbar that says how many tasks are available - just like the lucky moderators get.
Or, as Knights suggested, hover text could be used. On mobile, however, hover doesn't work. I'd vote for hover text when on a Desktop platform and an (unobtrusive) number when on Mobile.
Preferably, this number would not be some emergency color, like red or yellow, but maybe blue or light green. The idea isn't that we are instantly notified - there's thousands of us to handle this stuff - but that we can see how tasks there are without clicking a link.