Lightswitch to Outside Light/GCFI Issues
The load is at the top of the photo this is where the wires to the light go. The line is at the bottom of the outlet this is your incoming hot and neutral. 

Why is there black heat shrink on the whites at the GFCI the black on the white is designating the white as a switch leg and it should always be hot, if you put it on take it off. 

With switched circuits a switch leg is where the power comes into the lamp not a switch. We use a cable black white to run down to the switch, the white is connected to the black hot so the white is always hot and marked with tape , marker or any means to designate it as the hot. The black is then the switched hot.

Only having 2 cables at the outlet make sure the load goes to the lamp and the line is the incoming power. 

With the photos my guess you switched line and load and that won’t work.