How would baking time need to be adjusted if baking a gluten free cake in an angel food cake pan versus 9" round?

I'm with Kristen. Whatever the bake time is for the conventional cake, set a timer for 15 minutes less, then begin testing it for doneness by judging color and tapping the surface. If you have a thermometer, the cake should read 185 degrees at its center when done. Add baking time in 5-minute increments until your cake is done. To cool it, turn the tube pan upside down over a wine bottle.

It may bake more quickly since heat will be travelling up the center of the pan -- I'd check with a cake tester early.