In reference to this song speaking of biblical truth, I believe Amazing Grace has the understanding that Jesus has saved the author, a wretch who feels lost and blind and liberated him from a life of salvation. He went through many toils and tears meaning he has been through the worst scenarios he can think of but was able to find his way home by the Grace of God.
In the verse "I was blind but now I see.." shows his receipt of the gift of discernment. I do not see where theological profundity is shown in this song but the idea of being saved is present in the authors being lost and then found. Becoming saved and bright shining as the sun shows his feeling about his new salvation and he has discerned that Jesus or God does exist which could support some theological arguments.
I do feel the song has a sense of strongly melodic prose and it's rhyming words guide the viewer to want to also find salvation for themselves. Of course, Amazing Grace is well known for being one of the most beautiful songs ever sung in the church so there is no doubting it's beauty. Not only is it beautiful but it is a simple testimony of a man to the beauty of Jesus's power of salvation.
Here is an article about 8 things AMAZING GRACE can do for you. Click the image to go to the article.