Is there a specific word for the name of the part of the wagon highlighted in red? This is towards the rear.
On a Conestoga Wagon, the museum folks have it as a "rear end gate". See the third drawing, section c (labeled figure 10).
Figure 10.—Details of the Freight-Carrying Wagon, 1800-1820, of Figure 8. (Drawing by Donald W. Holst.)
a: Feedbox: 1, Top. 2, Side, showing pin and lug for securing to tongue. 3, End, showing bracket into which the chains hooked for traveling.
b: Front end panel: 1, Bottom end rail. 2, Middle end rail. 3, Top end rail. 4, Standard, or upright, forming end framing. 5, End boards. 6, Bow. 7, Corner plates.
c: Rear end gate: 1, Staples for end-gate standards. 2, End-gate hasps and hooks. 3, Pins to secure gate to upper side rails. 4, Crossbar to give extra support to end gate.
d: Rear wheel.
e: Cross section of wheel: 1, Boxings, of cast iron, wedged in hub to take wear of axle.
f: Front wheel: 1, Felly, or felloe. 2, Spoke. 3, Hub, or nave.
g: Floor of wagon, from under side: 1, Crossbeams, the center and rear ones being heavier, and projecting at the ends to hold the iron side braces visible in figure 8,a. 2, Bottom side rails. 3, Floorboards. 4, Position of rear bolster when bed is on running gear. 5, Front bolster, showing hole for kingpin.
Source: Research and Text by Bryan Wright
My first thought for the answer was tailboard, and indeed that is attested:
A hinged flap at the back of a truck that can be lowered or removed when loading or unloading the vehicle; a tailgate.
‘A tailboard from a trailer was lost on Sunday, November between 8pm and 9pm on the Stradbally Road.’
(Their definition of tailgate is actually identical, but then that particular bit has two names.)
It is, as on many other vehicles, a tailgate.
For example See https://www.pinterest.co.uk/pin/428827195745127778/