As early as possible or as late as possible. For early wagers the Pinnacle overnight line is very useful, because they use every digit (100,101,102,103, etc), instead of just 105, 110, 115. So Pinny is more sensitive. When the early Pinnacle line is about to move a half point (e.g. 105 lines now tilted 110 and 100), or has just moved, a book with a slower response time can often be caught watching. Don't ask which books.
Even if you don't really like the bet, it may be good to take it anyway. If you add a book like Skybook (free 1/2 pt), you can usuallly get a middle at a full point. If you do shop for middles remember that 1/2 pt lines are more profitable than full point lines. You can win both sides in a 6.5 and 7.5 middle, but only one side in a 6 and 7 middle, where the second bet would end in a push. Downsides: the line can move the other way, and Skybook only offers free 1/2 pt NBA wagers up to $300.
Middling doesn't have to be with even amounts. I hit one yesterday with most money on SAC -8.5 and much less on HOU +9.5, placed because large home faves often leave the backdoor open. SAC was up by 15 with less then half a minute to play, then gave up two 3-pt shots, to win by 9 pts.
So I'm not suggesting that all games are good targets for this approach. In my experience this only pays in basketball, where the margins are soooo slim. In the NFL it wouldn't make much sense.
Just thought I'd throw that in because you asked about line movements.