Monitor the remaining duration on your Mysterious Eggs and other perishable items. These items (and their durations) will be hardcoded in as they are requested. Items are only properly detected when you first receive them. Item detection is disabled when the Trade window is open, in order to prevent detecting old items.
This is an Ace3 addon, with support for LibDataBroker. A minimap icon is available for those without a broker display.
If you are experiencing tooltip duplication with DockingStation, be sure to disable DockingStation's tooltip scaling features for EggTimer.
Version 0.4 has been largely rewritten and will lose your data from 0.3. However, we have nice Consortium information now, and new features will be much easier to add in future.
Version 0.3 prompts you to create a Calendar event for when your egg will hatch. A summary of perishables on any of your characters is available on the FuBar/LDB/DBIcon tooltip. You can configure announcements so you'll be notified when your items expire.