Regarding many of the commonly sold morning glories, as long as the support isn't too wide, they can twine around on their own and by about 4" - 6" tall, they can start twining.

My balcony has a "shell pattern" fencing between the posts, so my morning glories can usually grow through the holes and twirl around as they grow upwards. I usually guide them for a bit and afterwards, they do it all on their own. A number of years ago, I had run some strings along a trellis that I secured to the rail, to give the various climbing plants that I grow in a trough box (usually the morning glories, sweet peas, scarlet runner beans, etc) a place to start before they get to the fence. The trellis reaches about 3ft above the rail, and I even put some additional florist wire above that to form an arch at the top that the vines can twirl around.

Generally, the vines will reach for the light and will aim towards the railing anyway. It's just a matter of getting them started when they are small. The fishing line is just another support that could be used if you want them to go a certain place.