My MIL makes it thin and crispy. Don't know if this is what you are looking for but here is how she makes it.
2 TBS of corn meal
1/4 tsp of salt
3/4's cup of water
Mix this together and it should look like milk replacer.
Take a #9 cast iron skillet and heat 2 tbs of bacon greese in it until its almost smoking. Agitate skillet to get some of oil on the edges - about 1/2 inch is plenty. Pour mix in center and then turn heat down to about 4 on the range. Watch the edges for doneness. When the edges begin to brown test to see if the cornbread will flip. If so, flip and cook till done.
She also makes a cornmeal prawn that is pretty good too. Texture of a dog bisquit but tasty nonetheless.