the Customizer – proper way to instantiate an image upload control via javascript

You would just need to add a canUpload: true to your control’s options (the 2nd parameter for wp.customize.Control) and then the .actions div would have an upload button.

However, clicking the button would not do anything (the media modal/popup would not appear), hence you need to instead use the specific class for image upload control, which is wp.customize.ImageControl.

Working Example (tested with WordPress v5.9.3):

wp.customize.control.add( new wp.customize.ImageControl( myControlSettingID, {
    section: 'issue_section_term_apple_section',
    label: 'Custom image',
    button_labels: {
        select: 'Select image',
        ...
        frame_title: 'Select image',
        frame_button: 'Choose image'
    },
    canUpload: true,
    setting: wp.customize( myControlSettingID )
} ) );

Remember though, that the image upload control will return only the image URL, so if you need its ID, then use new wp.customize.MediaControl instead.

References, or resources that might help you further:

• The WP_Customize_Media_Control class (see the to_json() and get_default_button_labels() methods).

• https://make.wordpress.org/core/2017/11/01/improvements-to-the-customize-js-api-in-4-9/

• https://developer.wordpress.org/themes/customize-api/the-customizer-javascript-api/

• and the source code of wp-admin/js/customize-controls.js (see lines 7875-7881).

As for this:

I am trying to toggle this control based on the value of another
control. Will I need to manually bind the controls together?

Excerpt from the 3rd link/resource above:

There are also activate() and deactivate() methods now for
manipulating this active state, for panels, sections, and controls.
The primary purpose of these states is to show or hide the object
without removing it entirely from the Customizer.

So if that’s your purpose, then you can use the above methods, like Twenty Twenty-One did, like so: (see assets/js/customize.js)

// Wait until the customizer has finished loading.
wp.customize.bind( 'ready', function() {
    // Hide the "respect_user_color_preference" setting if the background-color is dark.
    if ( 127 > twentytwentyoneGetHexLum( wp.customize( 'background_color' ).get() ) ) {
        wp.customize.control( 'respect_user_color_preference' ).deactivate();
        wp.customize.control( 'respect_user_color_preference_notice' ).deactivate();
    }

    ...
} );