Take a look at
www.alpa.org. You will find the latest and greatest about rest / duty times there.
In short, the Federal Register May 17, 2001 stated that you cannot extend your duty time for ANY reason. Your ops manual must say when your duty begins and ends. Commonly 30-60 minutes prior to scheduled block out and 15 minutes after actual block in.
Your example of having 1:15 left of duty time. If the ETE on your flight release is 1:00 and your takeoff is not delayed, then you are legal. However, if you are holding short of the runway and based on information that is available to you, realize that you will exceed your duty time, you could NOT legally depart.
I have copied and pasted the below info from ALPA.ORG.
Important FAA Interpretation Limits Maximum Continuous Duty Day to 16 Hours
The Federal Aviation Administration has closed a regulatory loophole used by some airlines to keep pilots on duty indefinitely. The November 20, 2000 ruling by the FAA’s Deputy Chief Counsel interpreted 14 CFR 121.471(b), clarifying that 16 hours is the maximum time a pilot can remain on duty, regardless of delays caused by weather, air traffic control, or maintenance.
Current domestic FAA regulations limit scheduled flight time to a maximum of eight hours in a single duty period, with an exception allowing the eight-hour limitation to be exceeded "due to circumstances beyond the control of the carrier." However, another rule requires pilots to "look back" after every arrival and find at least an eight-hour scheduled rest period during the previous 24 hours.
In a recent FAA interpretation, FAA Deputy Chief Counsel James Whitlow wrote, "If, when using the actual expected flight time [for a segment], the carrier cannot find at least eight hours of look-back rest upon arrival, then the flight may not depart [on that segment]."
With regard to delays, the interpretation states, "If, when this information is factored in, it is known or should be known that arrival based upon the actual expected flight time will not result in at least 8 hours of look-back rest, then the flight may not leave the gate. If the flight is away from the gate, but not yet in the air, then the flight may not take off." The ruling therefore requires pilots and airlines to continuously monitor delays, particularly during lengthy duty periods, to ensure that a flight will not violate the rest requirements under the FAA regulations.
Full text of the letter dated November 20, 2000 from FAA Deputy Chief Counsel Whitlow
Hope this helps.
Fly Safe,
Corp Pilot