First timer

SmokeDiesel, welcome to SMF!  Glad you're here and jumping into the deep end with smoking a brisket. 

225F/107C works just fine for brisket, but so does 250F/121C, 275F/135C.  The only real difference between the three temps is the amount of time it takes for the brisket to get to a final temperature and tenderness.

A brisket can be an ornery cut of meat.  It is done when it is "probe tender."  That means a toothpick, dual pronged fork, instant read meat thermometer, anything pointy you stick in the meat slides right in like it would into room temperature butter.  Some briskets are probe tender at 190F/88C, other's not probe tender until 205F/96C.  Personally, I find that 200F/93C works for the majority of my briskets that I intend to slice.

When he said "try to keep the meat at 136F/58C," there might have been a bit of a misunderstanding.  There is something called the "danger zone," which is 40F/4.5C to 140F/60C.  Meat needs to spend no more than 4 hours in that zone on the smoker.  It is important in your case because you injected the brisket.  Injection is just fine.  It does compromise the integrity of the muscle and pushes surface bacteria deep into the meat.  That bacteria multiplies in the 40-140F range after 4 hours.

You didn't say the weight of your brisket, but a smoker in the 225-250F range will get just about any size cut of meat through the danger zone. 

The reason I mentioned weight is that will impact your cooking time.  Based upon your planned start and finish time I'm guessing the weight of your brisket, probably the "flat" portion of the brisket as opposed to the "point," is about 4 lbs, or 1.81 kg.  Really, that's the only part of your scenario that is missing.

Enjoy the forum!

Ray