1. An image capture control apparatus comprising:a touch detector configured to be capable of detecting a touch operation; and
a memory and at least one processor and/or at least one circuit to perform operations of the following units:
a tracking unit configured to track a tracking target in a live view image captured by an image capturing unit;
a display control unit configured to, in response to the touch detector detecting a movement operation of moving a touch position, carry out control to display an indicator at a position, in a display, that is based on a movement amount of the movement operation,
a control unit configured to, in response to a predetermined amount of time elapsing after the touch for making the movement operation has been released, carry out control such that a tracking target determined on the basis of the position of the indicator is tracked by the tracking unit; and
an object detection unit configured to detect a specific object from the live view image,
wherein the control unit carries out control so that if the indicator is near the specific object, tracking is started immediately, without waiting for the predetermined amount of time to elapse, in response to the touch being released, and if the indicator is not near the specific object, the tracking is carried out after the predetermined amount of time has elapsed.