It's maybe not quite as simple as the other posters have suggested.
Hooking the sticks directly to devices to generate a pulse train to move
the servos will result in something that works, but the sticks will
control position not velocity.
The servo will position itself at the speed the joystick is
positioned, fast stick movement for fast servo movement, slow
stick movement for slow stick movement.
Sticks central is point straight ahead, if you want it to point to a
specific spot, you've got to hold the joysticks on that spot. (assuming
a central return stick)
You probably can use the buttons on the stick to switch the
pulsed output on and off using something like a small double
throw double pole relay. A setup could be two 555 chips, one for
up/down, and one for left/right control. The pulsed outputs from
these two chips go through the relay that is closed contacts when
the stick button is pressed. Press the button and move the stick
to position the two servos as desired, then release the button
and the servos stay where they are and the stick can return to
the neutral position. Send the relay outputs to a 6 position dual
contact rotary switch so that up to 6 pan/tilt cams can be
individually selected. I haven't used the 555 chips, but I've
done much the same thing with a joystick connected to a computer
to control my DIY servo pan/tilt cam (below).
http://www.geocities.com/zoomkat/ezservo.htm