Deadheading is considered duty, so it is part of the duty period, not part of the rest period.
Each duty period is composed of several parts:
- a report time, defined in a specified timezone (perhaps GMT, perhaps local, perhaps "home" time of some sort)
- time from the report until the first departure, which is typically standardized although it may be variable (45 minutes domestic, 60 minutes international, 75 minutes international overwater, for example)
- a series of flight legs, each with its start & stop times, duration, start and end airports, and deadhead status
- time between each leg
- time from last arrival until release from duty, which accounts for the time on duty required to post-flight the aircraft, clear customs, etc. This is typically standardized in some fashion; xx minutes if clearing customs is not required, yy minutes if it is
For each duty period that does not end back at the base, there will be the intervening crew rest period, or "overnight", which consists of the start and end times of the rest period, its duration, and in practice a specified hotel where the crew will stay.
The pairing itself will typically be published with some summary values, such as total flight time during the pairing, total duty time in the pairing, etc. If the crew contract specifies "overrides" for pay purposes, these will generally be published as well. As an example, let's say that the contract specifies pay credit of 1.2 minutes paid for every minute of block time between the hours of 2300 thru 0500, and a particular flight operates from 2200 to 0100. That is 3 hours of block time, but the last two hours pay at 1.2x, so the pay credit for that leg would be 3.4 hours, or 3:24 of pay even though it's only 3:00 of block. Other contractual rules may specify a minimum pay per duty period, such as 4:00 pay, even if less flying than that takes place. The pairing summary would generally include the total pay credit for the trip; each day's summary might include how that day's pay works out.
The rules of FAR Part 117 specify legal requirements for duty and rest periods; they include the definition of a "Flight Duty Period", which begins at the required report time, and ends at the block-in of the last operating leg. Thus, FDP ends even when a crew remains on duty. If the last leg of the day is a deadhead, then the FDP might be six hours but the duty day might be longer -- say an hour's ground time, and hour's flight, and 30 minutes to clear customs & leave the airport. When the crew is off duty, then the rest period begins.
Depending on the operation and the contract, the pairing details may align closely with Part 117, or there may be enough additional considerations that what's published on the pairing may go way beyond the Part 117 definitions. The FDP as defined in Part 117 (along with the other limitations in that regulation) are still tracked, although in some cases contractual constraints may be more limiting or require more bookkeeping (i.e. accounting for pay rules and contractually required rest periods).
When you're looking at things from the perspective of a Fatigue Risk Management System (FRMS), there are other factors to consider. Not everything that is legal is necessarily safe, and just because some sequence of duty periods is legal doesn't mean it won't be really fatiguing. For example, a sequence of 11-12 hour duty days flying in the same time zone may be fine, while the same sequence of 11-12 hour days crossing 5-6 time zones will shortly have the crew operating on the "back-side of the clock" in local time, which has its issues. Worse, if each 11-hour day is followed by a 16 hour overnight, the crew could be waking up later & later (relative the their body-clock time), but operating earlier and earlier in the day (as measured by daylight/nighttime looking out the window) -- which is a serious setup for "not knowing what time it is". An FRMS would probably need to consider how well or poorly a pairing or set of pairings works when considered against circadian rhythms and similar factors. This would involve tracking data beyond what is published for the typical crew trip-sheet.
At a minimum, you might want to see flights and days and rest periods considered in both a constant (say, "home" time) reference and also a "local time" reference -- even if what is published to the crews is all stated in Zulu time.
The question was asked in comments, when does Block Time begin & end? When the schedule is being built, Block Time corresponds to the scheduled departure and arrival times of the flight. The book definition of block time is that it begins when the aircraft begins forward movement under its own power for the purpose of flight, and ends when it comes to rest with no further movement intended. In practice, block time is almost always recorded by ACARS, which uses "all doors closed + brakes released" -- i.e. the start of the pushback operation -- as the block-out time, and "entry door open" (i.e. pulled into the gate and door is opened to let people out) as the block-in time.
This practice slightly over-states the block time as compared to the book definition, since one can release the brakes, then begin the pushback (under tug power, not aircraft power, and not "forward movement"), start engines, and so forth, and several minutes may elapse before the aircraft actually moves forward. And, if you arrive at the gate but the jetbridge isn't quickly pulled up to the aircraft, you may be stopped for some length of time before the ACARS records the "in" event. These distinctions are evidently acceptable to the FAA, since this seems to be a fairly universal practice to use ACARS times.
Typically, the reporting from the aircraft back to Dispatch or headquarters will have "out" (i.e. out from the gate, block time began), "off" (i.e. off the ground, flight time began), "on" (i.e. on the ground, landed), and "in" times. The aircraft logs are mainly interested in flight time, from "off" to "on", while crew recordkeeping is pretty much exclusively interested in block time, from "out" to "in". When FAR 117 refers to flight times, it is actually referring to block time "out" to "in" and is unconcerned with actual takeoff & landing times. One explanation being, the crew is as much responsible for the operation of the aircraft while taxiing around JFK on the ground, and needs to be alert in order to avoid mistakes (entering a runway without clearance, for instance), as much then as when they're in the air. So all "operating" time counts the same, on the ground and in flight.