Notice: Mount Olympus is a required parallel install to make Harpocrates work. Visit the linked page for more information.
Without getting into a lengthy dissertation on browser security, Harpocrates is a necessary plugin that works around emplaced limitations for things like cross-domain information sharing and use of GreaseMonkey functions.
What this means for you is that this script can save a timestamp when you login to Mechanical Turk and keep track of when you will be forced to logout. This is an extremely annoying problem to attempt to submit or accept a HIT and be met with a login window instead.
What it also means is that Harpocrates must be present on the Amazon login page to save the time you logged in, because there is literally no other way to get this information. Anyone with programming knowledge can clearly see the lack of nefariousness, but anyone without the requisite experience who doubts the safety of using this script should simply not install it.
Harpocrates inserts a simple line of text at the top right of the screen, and this screenshot also shows the tooltip that appears if you hove your mouse over it:
The text will also turn red when you're down under an hour:
The red text will also pulse when you're under 30 minutes.
The timer updates every 60 seconds to keep the countdown reasonably correct as the page remains open.