You shouldn't have any major issues using DirectRT to trigger / communicate with the eyetracker system.

If you visit this link:

http://empirisoft.com/directrt/help

Then click on 'search' (it's in the top left area of the page' and enter 'TTL' you'll find examples for syntax, etc.

It mostly depends on which pins in your PC's parallel port you want to activate, and what durations, etc are required. Probably the eyetracker system is looking for a certain pin to go high or low (have a 1 or 0 written to it). Check the documentation for the eyetracker system to see which pins are required.