To the original question, you need a voltage regulator circuit, they are very simple to create, using an LM317 regulator to bring the input voltage to a safe operation level with the Parralax model.
Google for schematics, they are common!
This 4 pin unit has a cds connection, meaning not only will it operate with motion, but can be hooked up to be reactive in light or dark, depending how you add a cds photo-resistor element.
Since you would be hooking to the picaboo or pickaxe and want 12V operation, you can feed the futurlec models (3 pin
here that will work just as well for 50 cents less per unit) without any regulator, it will funtion with voltage in that FULL range.
It doesnt matter that the parralax is a different voltage model than this. BUT you MUST regulate the voltage to 5V as mentioned above - more parts, more work. If you hook the parralax to 12V you will let out the magic smoke, and the PIR will be useless.
Since it uses TTL signal to activate whatever sub routines you want it is a matter of telling the controller how to percieve the TTL.
So don't guess, it is source voltage ground TTL out and CDS, if you hook it up as NO or NC it will not work.
You could hook the TTL to a logic signal controllable relay that has NO or NC contacts.