Ted Callaway testified that after hearing the five gun shots, he ran out to the sidewalk on Patton. This was a little over a half block south of the shooting scene. Callaway saw a man (who he later identified as Oswald) cutting across Patton as he (Oswald) made his way south on Patton (towards Callaway's position). Callaway hollered out to the man as the man continued south on Patton past Callaway's position. Callaway testified that the man was running and holding a gun. Callaway saw the man head west on Jefferson (the same direction as the theater).
Once the man turned west onto Jefferson, Callaway ran a "good hard run" up to the corner of Tenth and Patton. Callaway, noticing the stopped patrol car, went to the car and saw the officer (Tippit) lying dead in the street. Callaway said the first thing he did was to grab the police car radio and report the shooting. He said he didn't know if anyone had reported it yet, so he decided to report it himself.
To recap, Callaway hears the shots. Runs to the sidewalk. Sees the gunman run south on Patton the entire block from Tenth to Jefferson. Runs the two-thirds of a block up to the shooting scene. Goes over to the police car and the first thing he does is grab the radio and report the shooting to the police dispatcher.
How much time do you believe passed from the time Callaway heard the shots to the time he reported the shooting on the police radio?
Let's say two minutes pass from the time Oswald shoots Tippit to the time Oswald turns the corner from Patton onto Jefferson. This is a little over one block and Oswald was running.
Let's say it takes Callaway one minute when he made the "good hard run" the two-thirds of a half block from his location to the patrol car.
If these two time estimates are anywhere close to being correct, then Callaway is at the patrol car roughly three minutes after the shots rang out. Let's add another full minute for error. So we have Callaway at the patrol car using the police radio about four minutes after the shots rang out.
Here's the thing... Callaway's report to the dispatcher while using the patrol car radio took place at 1:19/1:20.
Do the math and work it backwards. At 1:19/1:20, Callaway makes the call. If four minutes have passed (and that's being generous, in my opinion) since the shots rang out, then the shots rang out around 1:15.