12.4v is about 75% charged, not enough to keep it from starting, or cause issues as long as when it starts the alternator functions properly.
What the alternator puts out as far as a charge varies, depending on how fast the car is idling, or how much of a load is being drawn.
Your battery could use a bit of a charge, see if you can get it charged up to 12.6v.
I am not sure how O'Reilly'* does it, but they should be able to test the alternator, and the battery while still in your car, that is how the other AutoParts stores I have been to do it.
I am pretty sure your ECM is on the passenger side, under the hush panel, on 94'* that is where it is, not sure as I have not seen one on a 93'
It should look similar to this.