Most calls start with something you can see. The mortar turns sandy when you rub it, it has pulled back from the brick face, or hairline cracks run through the joints. On older brick homes it's usually worst under a leaky gutter, around a chimney or near the ground where water sits. Those joints are the wall's first defense against rain, so once they open up, water gets behind the brick.
The price turns on how many joints have failed, how high the wall goes and whether it needs scaffolding, how hard the old mortar is to cut out, and whether something else needs fixing first, like a downspout dumping on the wall or a cracked brick. The schedule turns on the same things and the weather, since we don't lay mortar in the rain. Your written estimate lays out the materials, the steps and anything not included.
In South Carolina, repair of brick, block and masonry falls under the state's Masons trade, and when that work for a property owner runs over $500, the state treats it as residential specialty contractor work that calls for a license. Ask any crew you're comparing to show you theirs before they set up.