I don't have the exact code for you but you might try something like this if you are using GPS position averaging for vertices.
Use the OnAverageStart event of the GPS object to run a code that will get and hold the GPS time in a variable that is accessible out of scope. Since this code will run with each new positioning averaging event, you will need some code to restrict the time capture to the first averaging event. Then perhaps at the OnFeatureAdded event, you can capture the end time, write the start and end times to appropriate fields or what have you and clear out the global variable that holds the beginning time.