How to manage time spent

I need some to help me with how they keep track of time spent. Our current system gives us nothing right now. One of the reason I would like to switch is because of the reporting.

A ticket is open and sits in open status. A tech starts the ticket and time is kept unless marked as closed or on hold. The problem I have is there is no time spent listed on ticket details. The only way I can see the amount of time spent is to close the ticket and then go back and add a time entry. This was the case in the old version which I aslo brought up. Is there anyway to automate a time entry when the ticket is closed.

If you run a report without a time entry there will be not entries until you go back and add the time. So as I see it the process is

Ticket Opened
Tech Assigned Ticket (marked as open)
Works and completes ticket
Tech has to go back into ticket after closed to see time spent
Add time entry
Now Time reports show correctly