There's a bit of ambiguity about this subject that I'd like a clear interpretation of, too.
I've always used the method described above by thpaulsen, the moment a/c 1 starts to accelerate down the runway, note the time, and that becomes the reference for following departures. (As a technique, personally I make a mental note of the time, and/or write it to the nearest 10s on the strip, but some use an electronic timer.)
Thing is, though, it does state "at the time the a/c is airborne.." (or similar) so unless you know exactly how long a/c 2 is going to take to get airborne, it becomes a guess. Which means it's a guess. (As several posters to this thread have alluded, and use, and it's probably a more than adequate guess.)
I would think the lawyers would argue that since the only reference you can be sure of is the time you observe a/c 1 lift off (or rotate) that timing should commence from that moment, and a T/O clearance not issued to the following until the required time interval is up. That would (perhaps) be a purely legal, pedantic view.
In practice, that would certainly do nothing beneficial for efficiency, of course. Unless all ADC started actually doing it in an effort to get the ATS OPS folk to re-write the rule, or provide a clearer interpretation.
So in practice, all my timings commence at the start of the takeoff roll, and 99.?% of the time that will be adequate.
(Where it may not be is the situation where a very slow medium or heavy is departing in front of a real zippy light. Think, maybe, Argosy departing ahead of Learjet. #1 = 50s~ to accelerate to Vr, #2 maybe 25s.)
Re when the vortices start/stop, for landing, it seems to me that once the mainwheels have touched, the AoA is reduced by about 3 degrees, which will immediately reduce but not eliminate the vortex. A second or two later, though, the spoilers (when fitted) will pop, and the vortices will immediately be reduced by a very significant amount. The nosewheel then comes down, and in theory, no more vortex.
For takeoff, the spoilers should not be up and the moment the aircraft starts to rotate, vortices are being produced. I would think their intensity would be at its greatest at or just prior to liftoff, unless fuselage length precludes the best rotate angle for lift until clear of the deck.