OK, the "Use item" binding was the missing link.
Proper configuration does the trick.

Thanks for your help

it's not about targeting, it's about firing. When you're in targeting mode but assigned RMB to 'Clear Cursor' you cannot fire.

Firing Artillery is fixed to Right Mouse Button and cannot be reconfigured. When you used RMB otherwise, e.g. 'Clear Cursor' then you cannot fire Artillery anymore.