PRIME CANDIDATE FOR MAN IN LIGHT BROWN JACKET ENCOUNTERED BY OFFICER BAKER BY REAR STAIRS SEVERAL FLOORS UP IN TSBD:

PRIME CANDIDATE FOR TAN JACKET MAN (=SHOOTER OF OFFICER TIPPIT):

Whether it really is this guy in both cases, or someone matching his description remarkably well, there is a simple fact about him that distinguishes him from Mr. Oswald:
between Dealey Plaza and Oak Cliff, he has not changed his clothing.So IF Officer Tippit pulls over and talks with him, for whatever reason, HE will understandably fear/infer that the cop he encountered by the stairs in the Depository just after the shooting gave his full description, leading to a police radio broadcast. He feels especially exposed, and is panicked into shooting the officer.
It is
very possible that this guy---------Tan Jacket Man----------finds himself in much the same situation as Mr. Oswald. He signed up for a White House-approved false-flag missed-shots incident, performed his part faithfully from the SN window, only to discover with horror just afterwards that something much more nefarious was going on: an actual assassination. If so, then the man encountered by Officer Tippit on Tenth St. is,
just like Mr. Oswald in the Texas Theatre, a 'guiltocent' man on the run from the cops.
What's he doing on Tenth St.? One answer might be: going to catch a bus for Red Bird Airport. He's the LHO-resembling 'Oswald' whose flight 'to Cuba' was to be a core element in the original planned story fed to the world by the Kennedy administration. Despite what just happened back in Dealey Plaza, he's sticking with the plan.
But after the lethal encounter with the officer, he's a cop killer to boot. All bets are off. So he flees down Patton a little ways before turning into the alley, as seen by i.a. Ms. Helen Markham, and by Mr. Bill Brown's least favorite witness, Mr. Jimmy Burt@1963: