Just tested...

Invig:
We are assuming you hit every GCD in the 20sec sprint plus 10sec downtime, that leaves you with 340 TP which gives you a stupid 6s sprint.
If you just hit GCDs in the 20sec sprint and not in the 10sec, you are left with 390 TP so 9sec sprint.

Obviously using Enhanced Enliven changes this and using TP restoration items gives an even more crappy 2nd sprint

To say Dragoon has no TP management (or any melee for that matter) is silly.