@awnlee jawkingThe problem you're going to run in to here is that gawk is not a particularly common word, which in turn means that it isn't likely to have multiple forms*. It's simply not used often enough to go through mutations.
I'm having a bit of trouble finding the word lists I used to use, but according to Google's nGram viewer, "look" was at its lowest usage level in the 1930s at which time it was over 4,000 times more commonly used than "gawk". Even "ogle" is used more than gawk.
It is also worth noting that the word "gawky" does actually come from "gawk". Gawk means to gaze openly and stupidly (17th century), something is gawky if it is something you gawk at (18th century).
* In linguistics, a lemma is the base dictionary form of a given word, forms are its variations, and the lexeme is the underlying meaning that applies to all forms. For example, "look" is the lemma, "looking" is a form, and the lexeme is "to direct one's gaze toward someone or something or in a specified direction" (Oxford Languages).