From the moment he appeared on Sasuke's side to watch the show, to when he later rushed to Naruto's side and severely wounded Obito, scaring Konan away.
Finally, when he arrived at Jiraiya's side and destroyed Deva Path Pain, Hawking had timed it all precisely.
If he had not calculated the timing, with his speed, he could have made the rounds of all three battlefields and dealt with every enemy in less than twenty minutes.
His purpose in doing this was simple.
It was to deliberately demonstrate his value, making what he had done carry more weight in the eyes of the Hidden Leaf Ninjas and Tsunade.
Otherwise, if he had easily resolved everything in no time, his help would have seemed cheap instead.
It was the same principle as seeing a doctor.
If a doctor spotted the problem as soon as you fell ill and cured your disease with a simple prescription, you would feel that your illness was nothing serious and the doctor's skill was nothing special, perhaps not even worth paying much of a consultation fee for.
But if your illness had already nearly killed you before the doctor figured out what was wrong, then used all kinds of precious medicinal ingredients to save your life, you would definitely consider that doctor a miracle worker and willingly pay a great deal in medical fees.
In truth, if not for his bottom line, Hawking could even have waited until Konoha Village had been destroyed by Akatsuki before acting. That would have allowed him to gain the greatest possible benefit from Tsunade.
Still, he was not too worried that Akatsuki would immediately turn around and attack again after he disappeared.
He had not held back before. Even with Karin treating him, Sasuke's side could not possibly recover that quickly.