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My research group actually analyzed this very question a few years ago. We have found evidence for goblin DNA in the genomes of every species affected by this phenotype change.* Without a representative sample of pre-Gap remains available for comparison testing, we cannot conclude with certainty when this admixture occured let alone how, but existing records do suggest that the phenotype at least was not present before the Gap.
The exception is Akitonian ysoki. Pre-Gap remains we were able to analyze did not have any detectable goblin sequences. Given the volume of desert mummies we actually tested what we consider a representative sample of that planet's ysoki population. But of course we can only speculate if the same timeline (whatever it was) applied to the other affected species.
*When I say evidence I am not speaking of proof, but our confidence level was 4-6 sigmas for 91% of the sequences and 7 sigmas in 2% of them.
You can read more details in the Kashakian Journal of Modern Medicine, Series 8 Vol. 81 Issue 27.