I managed to ignore all symptoms until DS was tested at age 4 and I had to acknowledge the giftedness because of the numbers in the testing report staring me in the face. But, my husband is not convinced even now and he thinks that the testing numbers could have been an anomaly - because my son has asynchronous development, has a very atypical way of reasoning, has a slower processing speed than his parents, has poor motor coordination compared to his parents and is very different from the stereotypical gifted child. So, his giftedness is obvious only to his tester, his math mentor, his music teacher and his mother while even his father dismisses it because superficially it is not obvious.
But, the extreme giftedness rears its head occasionally in social and academic situations much to the shock and amazement of the disbelievers in my family.
As for the pediatrician, ours always ignored my queries about giftedness and I stopped asking! She did say that in order to help the sleep problems, my DS could either be medicated (melatonin or benadryl to make him drowsy before bed every night) or that he could be tired out to such an extent that he fell asleep. We chose the tiring out option and involve DS in very rigorous exercise everyday (sports, play, biking, running etc) and we get close to 7-8 hours of sleep from him.
