To expand on the approach @Aditya was hinting at in his comment, you
can chop whatever picture you choose as the background into fitting
pieces using the \clip macro.
First, set a partitioning grid using \setupclipping, e.g.:
\setupclipping[nx=2,ny=4]
This defines clipping to use two segments horizontally and four
segments vertically.
You can then address these parts using their coordinates:
\clip[x=2,y=3]{...}
This extracts the piece that is located at the third column of the
fourth row of whatever the macro is applied to.
Your doublesided background is a simpler problem as it requires only a
single horizontal split:
\setupclipping[nx=2,ny=1]
%% left half:
\clip[x=1,y=1]{\externalfigure[...][width=2\paperwidth]}
%% right half:
\clip[x=2,y=1]{\externalfigure[...][width=2\paperwidth]}
Now you just have to draw these parts as the background.
This is no problem in Context as all the elements that constitute the
page layout are derived from
\framed, inheriting its options.
Thus, in order to draw an image as a page background you can use the
same strategy as with \framed: wrap the content in an overlay and
assign it to the background.
The element that spans one entire page is called paper, and you can
configure it via \setupbackgrounds:
\defineoverlay [background:overlay] [\backgroundcmd]
\setupbackgrounds [paper] [background=overlay:background]
What’s left is to define \backgroundcmd so that it clips the left
or right half depending on whether the current page is recto or verso:
\def\backgroundcmd{
\ifodd\pagenumber
\clip[x=2,y=1]{\externalfigure[...]}
\else
\clip[x=1,y=1]{\externalfigure[...]}
\fi%
}
Combining everything, a solution could look like this:

\setupexternalfigures [location={default}] %% figure search path
\setuppagenumbering [alternative=doublesided]
\unprotect
%% 1) a named figure for inclusion, scaled to twice the width of one
%% page
\useexternalfigure [half_cow] [cow.pdf] [
width=2\paperwidth,
height=\paperheight,
]
%% 2) a command that draws the left or right portion of a figure,
%% depending on whether the page is recto or verso.
%%
%% also, we install a counter to check if the background should be
%% placed at all, since it is only desired with “\part” headings.
%% this counter will be decremented with every invocation and reset
%% whenever a new part begins.
\newcount\cowcount
\def\pickhalfcow_cmd{%
\setupclipping [nx=2,ny=1,]%
\ifnum\cowcount>0
\ifodd\pagenumber %% clip right half
\clip[x=2,y=1]
\else %% clip left half
\clip[x=1,y=1]
\fi{\externalfigure[half_cow]}%
\global \advance \cowcount \minusone
\fi%
}
%% 3a) define an overlay that we can use as page background
\defineoverlay [pickhalfcow] [\pickhalfcow_cmd]
%% 3b) hook the overlay into the “paper” element of the layout
\setupbackgrounds [paper] [background=pickhalfcow]
\setuphead [part] [
page=left, %% assumption: parts always begin verso
insidesection=\cowbackgrounds,
]
%% 4) define auxiliary macro that resets the background image counter
\def\cowbackgrounds{\global\cowcount=2}
\protect
%% Ready. Here’s some code that generates a couple pages.
\starttext
\startcolor[red]
\definedfont[name:IwonaMediumRegular at 22pt]
\setupinterlinespace[25pt]
\startpart[title=South America etc.]
\dorecurse{5}{
\input knuth \page
}
\stoppart
\startpart[title=Birds And Such]
\dorecurse{5}{
\input knuth \page
}
\stoppart
\stopcolor
\stoptext
Update:
Hooked the code into the part headings.