The brushes should run continuously along the whole length of your guttering. When one brush finishes, bend the excess wiring at the end of each brush backwards to form a hook and simply attach the two brush ends together to continue the run. The brushes can run directly across the down pipe or drain outlets.
If there is excess brush at the end of the run, cut the excess of with a pair of wire snips but make sure you leave approximately 50mm overrun, then untwist the wire to remove excess filaments, re-twist the spine and bend into a hook shape and secure into the gutter.