Sawyer says that he remembered a transmission on channel 2 saying that a gunman was seen in a TSBD window, but his memory is vague about the exact transmission. That would mark the latest time he was still in his car listening to the radio. The first such transmission on channel two is Haygood's at 12:35 (not 12:34):
Haygood: I just talked to a guy up here who was standing close to it and the best he could tell it came from the Texas School Book Depository Building here with that Hertz Renting sign on top.
Dispatcher: 10-4. Get his name, address, telephone number there - all the information that you can from him. 12:35 p.m.
The next is Harkness' transmission at 12:36:
Dispatcher: Attention all emergency equipment, do no use Industrial Boulevard......12:36
Harkness: I have a witness that says that it came from the 5th floor of the Texas Book Depository Store.
In the Martin film, you can see Amos Euins riding on the back of Harkness' three-wheeler eastwards from behind the pergola. They're headed towards Houston on Old Elm. In the background, in front of the TSBD entrance, a car pulls in to park. That car looks like the one that you think is Sawyer's. Harkness remembered the sequence like this:
Mr. HARKNESS - I found a little colored boy, Amos Euins, who told me he saw the shots come from that building.
Mr. BELIN - Now you just picked out a little small book, one of those little pocket notebooks?
Mr. HARKNESS - Yes, sir.
Mr. BELIN - Or a notepad from your pocket here. Is that the original notation that you made?
Mr. HARKNESS - Yes, sir.
Mr. BELIN - When did you make that notation?
Mr. HARKNESS - Immediately after the shooting.
Mr. BELIN - Is that your own record that you have kept in your possession since then?
Mr. HARKNESS - Yes, sir. I turned.
Mr. BELIN - You turned what?
Mr. HARKNESS - After I took his name and address and put this information on the radio, I then took him on the back of my three-wheel motorcycle and put him in Inspector Sawyer's car.
So if Harkness made his 12:36 transmission before he put Euins on the motorcyle, and the car in the Martin film belongs to Sawyer, then Sawyer could not have parked in front of the Depository before 12:36
BTW, this is the best online version of the Martin film I can find. Euins and Harkness (+subsequent paleophotobomb) appear about 0:50 in:
Nice one Mitch.
I was totally unaware of this most important synchronism.
As you point out, Harkness testifies to making his transmission and then taking Euins to Sawyer's car.
The transmission is at 12:36 and the Martin film shows Sawyer arriving as Harkness makes his way towards Sawyer's car.
This has important ramifications for Sawyer's testimony.
He testifies that he arrived outside the TSBD, talked to various officers then went upstairs to check the 4th floor before coming back down about 3 minutes later.
He arrives at 12:36 pm (not 12:34 pm)
Goes into the TSBD around 12:37 pm.
Comes back down around 12:40 pm.
It is not until 12:40 pm that he orders the lock down of the front entrance of the TSBD.
This appears to be confirmed by the Dallas Police transcripts that has a transmission from Sawyer at 12:40 pm
"We need more manpower down at the Texas Book Depository there should be a bunch on Main if somebody can pick them up and bring them down here."