Agog
Showing a curious or inquiring attitude; eager to learn or investigate.
They can be. Eager in some circumstances suggests anxious, impatient, or enthusiastic. Excited may not mean eager to do something, but for having done something.
eager, anxious, excited, enthralled, enthusiastic, avid, impatient
Keen, enthusiastic, intent, impatient, determined?
alert. avid, agog
worried or excited eager, keen, intent, yearning, impatient, itching, desirous
to be eager for knowledge of or curious about something
anxious, keen, hungry, impatient, itching, thirsty, enthusiastic, passionate, avid, fervent
You could say that a person who has a "continuous desire to know the why and how of things" is incessantly curious- incessant means without ceasing, continuous and curious means eager to learn, inquisitive.
. having or showing keen interest or intense desire or impatient expectancy
"Jignesh" is an Indian name of Gujarati origin, derived from the Sanskrit word "jignasa" meaning curiosity or inquisitiveness. The name reflects qualities of being curious, eager to learn, and seeking knowledge.
Other words to describe "unable to wait" would be impatient, eager or anxious.