Hi mulberry, WELCOME TO THE FORUMS !
Do you happen to know if this is a translation? "Snowdrop" isn't part of my vocabulary, and I spent many years in snow country. "Snowflake" is common, but doesn't seem to fit your phrases.
The gauk I know is spelled "gawk." My dictionary defines it as an awkward, oafish person; and gives an "informal" usage as to stare, like an awkward, oafish person. (We only used it this second way.)
Are we possibly talking about a flower, or a candy? If you could give us a longer portion of the text, it might help.
I guess a stirring would be some kind of gut feeling - an undefined emotional sensation - a sense of movement from within. Stirring can be simply mixing or agitating something, as with a spoon, or it can be sort of coming to life after a period of inactivity.
A striving would perhaps be a feeling that you need to be doing something special.
Edit. Okay, "snowdrop" is a spring flower (eurasian) which resembles an awkward, oafish person. (sorry, no picture.)