CRA does not specifically cover this occupation, and I cannot find a occupation code for an eyelash extension technician.
So, uncovering what the government wants to call an eyelash extension technician along with its code is impossible to find at their web site.
Here is some suggestions:
812190 - Other personal care services
812114 - Barber shops
812115 - Beauty salons
812116 - Unisex hair salonsYou can also search for your industry code using this website: http://www23.statcan.gc.ca/imdb/p3VD.pl?Function=getVD&TVD=1181553