Andy,
T&S cannot provide the time requirements for Start on a "timely" basis. Starters have to do this for themselves. We don't time the laps (T&S does that), but we do keep the time for the length of the sessions. If we had to ask T&S for an "official time", we would need to call the stewards on the F&C radio, have them ask T&S on the Race Administration radio, and then get an answer back via the reverse path. Way to inaccurate.
The starter has to display the checkered flag on the correct lap, and it can be a real guessing game if the time limit is being reached and the distance hasn't been covered. More than once, the decision to checker a race on a given lap based on time has come down to a matter of seconds (e.g. less than 1 or 2 seconds).
At tracks like NHIS, the timing line is in front of the timing building in turn 4, and the T&S people don't really know when the race starts and ends. Officially, the first lap starts when you cross the S/F line and ends at the timing line. Hence the line in the supps that the first lap will not be used for setting fastest lap or track records. At that track, the Starter also scores the final lap for T&S and we call T&S to tell them if there were any position changes between the timing loop and the S/F line.
At Lime Rock, the timing loop isn't at the S/F line either, but it is only a few ( less than 12) feet past the line so the error is small. However, there have been times where the first car to the S/F line was not the first car to be picked up by the timing loop. (Hint: Keep your transponder as near the front of the car as you can...)
As far as when the race was red flagged, the timing system MAY have the time fairly close, but it is a case of them being told that race was stopped and then the computer system being "adjusted" to reflect what is needed. (Yes, I spent a year in T&S running one of those computers when I had bad knees). Start stops a clock when the Steward calls for the red flag. (I say "A" clock, because we normally have three or four clocks running. If there is a red or black flag all, we stop one and keep another going.)
As far as the list of required equipment goes, you will find there are lots of useless things (equipment) required, and lots of things that are required to do the job that are not listed. The GCR isn't "up to date", and hasn't been for years. (see 5.5 for the list for each flag station.) Any request to the CRB to have those parts of it updated falls on deaf ears. For example, you may note that there is no mention of a number board, a "sound" board, a "1" sign, a "pace car" sign, an "ALL" sign for "Black flag all", or the requirements that we have pencils (to do lap charts), paper, a clip board or two, or any of the dozens of other things needed to do the job. The list is neither all inclusive or exclusive.
Of course, at a drivers school, I time sessions with my sundial.