How to make an onscreen timer graphic that counts down to different sections of the video?
This is a very simple effect that can be achieved using the Radial Wipe effect (which can be found in the Effects panel Video Effects > Transition > Radial Wipe)



Using the 'Transition Completion' set one keyframe at the start at 100% and the second keyframe for the end of the clip at 0%. To match the effect in the example you have shown, change the wipe to Counterclockwise and find a circle or ring shaped graphic to represent the timer.

In this case the static red ring should be place in the background with no effect applied and the moving white ring should be placed above with the effect applied.

You could even use the Video Effect 'Circle' under Video Effects > Generate to create the circle.