Homebrew PCBs

Some ideas I haven't tried:

Use a stainless steel stirrer such as is used for making milk shakes.

Make some stirrer vanes out of suitable plastic, drive them with small DC
motors (so you can adjust speed by adjusting the voltage).

Make a centrifugal pump out of plastic.  It doesn't have to be terribly
efficient, just needs to direct a stream of etchant across the board to be
etched.

Use an oscillating room fan, or a windshield wiper mechanism to move the
board around in the etchant solution.

Chemical supply houses have a combination hotplate/stirrer.  The stirrer
works by having a rotating magnet underneath the beaker, and inside the
beaker you put another magnet that is coated with some inert material.  You
might be able to use a "cow magnet" as the coated magnet.  These are fed to
cows to attract iron nails and stuff in the cow's digestive system and get
them out of the system.  (That's no bull :-)  I just called a veterinary
supply company and they sell a 2-inch coated cow magnet for $2.65.)

You might not even need the cow magnet.  Since the etchant is conductive, it
will try to stay stationary with respect to any magnetic field.  So, if you
rotate a strong magnet adjacent to the tank, the solution may rotate in the
same direction.  This is the principle that makes induction motors work.

Use a peristaltic pump, such as from scrapped medical equipment.

Cheers,
- Jan