Click and drag events happen when the user releases a mouse button. They cannot happen earlier, because there is no way to distinguish a click from a drag until the button is released.
If you want to take action as soon as a button is pressed, you need to handle button-down events.1 These occur as soon as a button is pressed. They are represented by lists that look exactly like click events (see Click Events), except that the event-type symbol name contains the prefix ‘down-’. The ‘down-’ prefix follows modifier key prefixes such as ‘C-’ and ‘M-’.
The function read-key-sequence ignores any button-down events
that don't have command bindings; therefore, the Emacs command loop
ignores them too. This means that you need not worry about defining
button-down events unless you want them to do something. The usual
reason to define a button-down event is so that you can track mouse
motion (by reading motion events) until the button is released.
See Motion Events.