When MouseKeys are on, how do I click or move the mouse using AppleScript?
There are tons of command line utilities to do this... and I'd reckon that going this route's your best bet... One benefit? is that these solutions should work, irrespective of whether or not &quot;mouse keys&quot; are on, right?  One of my particular faves is cliclick

Cliclick” is short for &quot;Command-Line Interface Click&quot;. &gt; It is a a tiny shell / Terminal application that will emulate mouse clicks or series of mouse clicks (including doubleclicks and control-clicks) at arbitrary screen coordinates.
Hence, it is a tool for automating / scripting things that cannot otherwise be scripted (for instance, using AppleScript). Other than GUI Scripting, it does not require &quot;Access for assistive devices&quot; to be activated in the System Preferences.

Usage:
$ cliclick c m

will &quot;control-click&quot; the current mouse location, but you can also specify the coordinates, shift-click, double-click, etc.  It can also return the coordinates of the mouse with a -q argument, and return the mouse to the original location (when specifying coordinates) with the -r argument.
In your case.. I guess you'd just...
do shell script &quot;cliclick c m&quot;
from inside your AppleScript / Workflow / whatever...
There's a GREAT post on this subject on MacWorld's site (née Mac OS X Hints) - that I've gleaned lots of good info from, over the years.  If you don't care for my answer you will surely find a solution you DO like, there... there's hacks to make everyone smile - from an Automator freak = to a grumpy C diehard.
Update:
There do seem to be some ways - to &quot;do it&quot; in AppleScript.. but they all seem to require knowing where your mouse is... which i assume you don't.  So in an embarrassingly nerdy play for some rep... I wrote this..
do shell script &quot;python -c 'import sys, time; from Quartz.CoreGraphics import *;

def mouseEvent(type, posx, posy):
  theEvent = CGEventCreateMouseEvent(None, type, (posx,posy), kCGMouseButtonLeft);
  CGEventPost(kCGHIDEventTap, theEvent);

def mouseclickdn(posx,posy):
  mouseEvent(kCGEventLeftMouseDown, posx,posy);

def mouseclickup(posx,posy):
  mouseEvent(kCGEventLeftMouseUp, posx,posy);
  ourEvent = CGEventCreate(None);
  currentpos = CGEventGetLocation(ourEvent);
  print currentpos[0];
  print currentpos[1];
  mouseclickdn(currentpos.x, currentpos.y);
  mouseclickup(currentpos.x, currentpos.y)'
&quot;

What the hell is it?

AppleScript calls 'do shell script'.
Which then calls Python - with a command line argument (-c) = that's been escaped and cajoled = to cooperate with A/S.
Python then &quot;imports&quot; CoreGraphics/Quartz, etc.
And defines some Cocoa-API/PyObjC methods for &quot;dealing with&quot; the mouse.
Python &quot;figures out&quot; where the mouse is.
And clicks! (down, then up)
As a bonus, it returns the coordinates of the mouse, 'if you were interested_.

Works 100% and isn't even THAT slow. Hope you like it!
Edit:
Here is the BASH one-liner, for purists / A/S haters.
echo -e &quot;import sys, time; from Quartz.CoreGraphics import *\ndef mouseEvent(type, posx, posy): theEvent = CGEventCreateMouseEvent(None, type, (posx,posy), kCGMouseButtonLeft); CGEventPost(kCGHIDEventTap, theEvent);\ndef mouseclickdn(posx,posy): mouseEvent(kCGEventLeftMouseDown, posx,posy);\ndef mouseclickup(posx,posy): mouseEvent(kCGEventLeftMouseUp, posx,posy);\nourEvent = CGEventCreate(None); currentpos = CGEventGetLocation(ourEvent); print currentpos[0]; print currentpos[1]; mouseclickdn(currentpos.x, currentpos.y);\nmouseclickup(currentpos.x, currentpos.y);&quot; | python