Tuckpointing or rebuilding a brick wall
Most walls I look at need repointing, not rebuilding, because brick usually outlasts the mortar around it by a long way. If the joints are failing but the bricks are sound, repointing the bad joints is the right call. When bricks are cracked through or loose, or the wall is bulging or leaning, fresh mortar won't fix that. I'll tell you if a section has to come down, or if an engineer should look at it first.
What drives the cost of tuckpointing
Labor is the biggest part, so the price follows how many joints need work and how deep the worn mortar goes. A wall you can reach from the ground costs less than a chimney or a tall wall that needs ladders or scaffolding. An unusual mortar color takes more trial to match, and raking out joints by hand around soft brick is slower than cutting them on a sturdy wall. Fixing a leak or downspout first adds to the job, but otherwise the new mortar can wash out the way the old did.