So Uplinker,
You're on a Runway where perf figures suggest a 500m margin for takeoff.
Figures predicated on 5 kt headwind. Vr is 140.
Passing 110kts your eagle eyed PM takes his eyes off the engine display and notices a 7 kt tailwind on the wind readout. Neither of you had noticed anything untoward on the speed trend vector or tape.
What would you (or your captain expect you to) do?
How much time would you want to spend watching the speed tape and trend to assimilate it while taking off?
I can't believe I'm answering this. You have a split second to look at the size of the arrow and the movement of the tape before back outside or to the engine parameters. You don't need to process a value or compute anything. Just long enough to get a feel as to how long until the next speed (100 or v1).
You only need to glance at the arrow.
Unless your ND arrow increases in size with the wind direction you need to read the speed too. If youve seen the arrow going all over the place when the outside wind is vrb at 1-2 kts at altitude you'll understand. How do you know if that sudden tailwind is 1 kt or 10?
To look at the wind vector (which is of dubious reliability anyway) gives you no extra information, takes your eyes away from other more important items, and distracts with the cognitive awareness for other decisions.
The second of time that the PM spends trying to work out if the wind has backed or veered, and what the subsequent headwind component has done would be much better spent looking at the engine parameters.
And regarding unexpected tailwinds on departure, thats what the windsocks are for. If it's saying something you dont like on a marginal runway when you're lined up exit and recalculate with conservative estimated figures.