"Go suck an egg" is a saying typically used similarly to "take a hike" or "piss off":
Hey, you going to help me with this or what?
Go suck an egg.
An few Ngram searches shows that "suck an egg" is only really used with the words "go" and "an" but I was not able to find any reference to the origin of the phrase.
An existing question on ELU asks about the origin of "teaching grandma to suck eggs" but none of the answers directly discuss this usage of "suck eggs". When did this phrase become a common statement meaning "go away"? Why was this random activity associated with the idiom?