This nifty little solution will let you calculate the time spent on pages that are not tracked in Google Analytics by default. These include both bounced landing pages and exit pages. Bounced pages and exit pages lack the necessary subsequent pageview, which Google Analytics uses to calculate time-based metrics.
Before you go on, read this excellent article by Yehoshua Coren:
REAL Time On Page in Google Analytics
Yehoshua gives a very nice use case for the technical solution I’m about to explore.