What is the origin of the cliche parodied in the
following piece:

"Those drums, those drums, those incessant drums!
They're driving me mad, MAD I tell you!"
Later, drums stop.
"I don't like it.  It's too quiet."

I don't think this is a parody of any one movie, but a reference to a
kind of scene that often appeared in films of the '30s and '40s which
were set on remote, primitive islands or "In Darkest Africa." Such
scenes generally involve a group of "civilized" white men who are
encamped near a group of "savages" the sound of whose war drums
discomfit the Europeans. I seem to recall a scene like this in the
original "King Kong."

The lines of actual dialogue from the original
King Kong movie are probably what I'm looking for, then.

The combination of the "drums" with the "too quiet"
cliche could have been mainstream comedic material from
anywhere between 1933 and before people started publishing
SNL scripts on the Internet...

A synopsis of the King Kong scene, from http://www.filmsite.org/kingk2.html

"They reach the vicinity of the uncharted, fog-enshrouded island after
making their way through the unmapped territory in the high seas. Ann
wonders how they will know if it's the right one. Denham says the
island will have a formation called Skull Mountain: "A mountain that
looks like a skull" - a forbidding landmark for a place. A lookout
reports breakers ahead. Anchor is dropped in a cove. Driscoll says
grimly, "that's not breakers. It's drums!" They hear the muffled sound
of drums and chanting in the distance. When the fog clears during
daybreak, Skull Mountain and the wall come clearly into view exactly
as described, "just like on my funny little map," Denham says."

In 'Island of Lost Souls' (1933), mind you, there's a scene when
Charles Laughton as Dr Moreau, hearing the distant sound of drums,
says a line which has passed into cliche: "The natives are restless
tonight." Any use?

sounds like something gene wilder would say.

I seem to recall the line being spoken in the 1964 movie "Zulu" in
which 139 British troops, most of the wounded, are surrounded by the
Zulu nation bearing down on them for a final charge.

IMDB
http://www.imdb.com/title/tt0058777/plotsummary

Then again, it might have been the movie Jumanji. There were deafening
drum beats that forewarned danger throughout the movie. At one point I
seem to remember Robin Williams character saying something to the
effect of "it's too quiet..." then yelling "STAMPEDE!" whereupon a
huge herd of various African animals suddenly appears and runs through
the middle of the house they are in.

IMDB
http://www.imdb.com/title/tt0113497/

Regards;
tutuzdad-ga

Thank you all for your help!  I'll be checking out "Zulu".
And even while I'm not getting a slam-dunk answer out of
these, it does at the very least make for an decent list
of old cult and near-cult movies to watch while stalking
the wily line.

Though I am sure this is not the original, here's an attribute: 

Michaelangelo: It's quiet. A little too quiet. Always wanted to say that.
["Teenage Mutant Ninja Turtles" (2003)]. 

(Source: IMDB, what else? <www.imdb.com>).

Two other possible contributing sources might be "King Solomon's
Mines" (1937), starring Cedric Hardwicke and Paul Robeson (in which
Robeson sings), and "Gunga Din" (1939), starring Cary Grant, Douglas
Fairbanks, Jr., et al.

hlabadie-ga