That was the time it took for Perez to come up to Buttons rear. I was in the understanding Withmarsh call came lap 59, so i missed 2 laps. Still, there was no indication whatsoever that Perez tyres where gone, hurting, damaged, you name it. Withmarsh didnt want him to overtake Button, and thanks to your link thats even more apparent now.
Firstly, Sergios messages come from Mark Temple, not Whitmarsh. Whitmarsh doesn't talk to the drivers during the race, in the same way no other team principal speaks to any other driver during the race.
Now to mess up the discussion regarding when the messages were sent as the TV messages are delayed. The broadcaster chooses which message to play, and also delays them so they are less important for the race teams. According to
McLarens own live commentary on their website the first message to Sergio “We're going to need the tyres in good condition at the end of the stint. Keep looking after them.” was between lap 54 and 56, when Sergio was still over 2.2 seconds behind Button, not when he had caught up to him. This was followed by “There are places to take at the end but we must look after the tyres.” when he had caught up to Button, which implies passing several cars in front, not just Jenson.
There was also these other messages posted by McLaren on their live commentary during the race:
"0.7s between Jenson and Checo now."
"Lap 61: Tight battle between Jenson and Checo, also close are ROS and DIR, GUT and RIC. Lots to see in the final five laps."
To Sergio - “The cars ahead are coming back towards you.”
To Sergio - “One more lap after this one. Be careful of flat-spotting.”
"Nose-to-tail for Jenson and Checo on this final lap. Which way is it going to go?"
"Jenson pulls out a slight lead – will he keep it to the line?"
"ALO wins his home grand prix, followed by RAI, MAS, VET, WEB, ROS, DIR and… Jenson! Then Checo and RIC"
I don't see anything there that tells us they were told to hold station, they tell us McLaren were watching the pair of them race. Now I'm sure you are now going to tell us all that it is all a big conspiracy, that McLaren spent the last laps posting fake messages and had Sergio race from over two seconds behind to running right behind Button, so destroying his tyres, all to cover up team orders.