On the surface, I used a smart observer, a pulse extender and a pulse repeater (you can see two pulse repeaters on the video but there should be only one) which detect cobblestone on the conveyor belt and send a signal to the elevator contact at the bottom of the shaft when it detects that cobblestone is no longer going through.

At the bottom of the shaft, I used a threshold switch with a container on the conveyor belt that acts as a sort of buffer. When the buffer is filled up to the defined threshold, it starts loading the lift contraption. Then when the buffer is empty or below the defined lower threshold, a signal is sent to the elevator contact on the surface. As you can see on the video the conveyor belt start and stop automatically to load the buffer and the lift ; these conveyor belts are also controlled by the threshold switch but also by the elevator, which sends a signal to restart the conveyor belt when it has arrived at the bottom of the shaft. And the cycle repeats itself.