Muratic Acid will eat away at the cement, so I read. This means that you probably can't leave it on the brick/joint too long or it will start to break the joint down before it gets a chance to 'work' on the brick face. Check around with a Mason or Brick Layer on how to best do this job.
And at the same time, test the 'cleaning process' on an inconspicious area first. If it goes well, continue on. BUT, do realize that you may have to do the ENTIRE face since you'll see newly 'cleaned areas' vs. 'dirty areas' if you don't do the entire face. If you're rinsing this stuff into a garden, it will kill if it isn't adequately diluted. (Maybe it will kill no matter what the water:acid ratio is.) Try not to wash this stuff down the sewer.