Can a GFCI power a light and a switch in this order?
What was done was called a switch leg the black hot from the GFCI was tied to the white wire in the cable going to the switch. Both ends the wire taped or marked to show hot. Then that re identified wire on one side of the switch and the black on the other back at the light the black wire from the switch is the switched hot Or connects to the black of the light.
Next the white wire from the GFCI is the neutral that goes to the white of the light.
Once these connections are made it should work.
Note this is now an old method of wiring and we are supposed to take the neutral down to the switch location (or feed the switch first is the easiest without needing expensive wire or conduit (smurf tube commonly used).