I looked at the service information and discovered that the questions that I asked may help to further determine where the problem lies. So please answer them when you get the chance.
First, before you do anything are you under warranty? If you are and the trailer wiring is not the factory pigtail, it could present some problems making the warranty claim if it is discovered that the problem is due to an aftermarket wiring installation.
Ok, assuming that you most likely are out of warranty, it would still help me to know what type of wiring installation that your Aztek has. The first thing I would do is go to a facility like an Auto Zone or a NAPA auto parts store or another auto parts store that offers a free code reading service. The parking lamps have a direct electrical connection to the Body Control Module (BCM) (Part of the reason why I do not prefer trying to splice into the taillamp wiring on the Aztek). A quick glance at the service information reveals some of the following codes for the parking lamps: B2587, B2588, B2628, B3840, and B3841. Each of those codes has a different path of repair. The key components in this circuit is the Park Lamp fuse #20 (which you found under the hood), the Park Lamp Relay (underhood fuse panel #55), the BCM, the headlamp switch, wiring, trailer wiring harness area, taillamp/parking lamp wiring and the underhood fuse box itself. It is possible that there may be no codes present. If that is the case, the problem may center around the headlamo switch.
Please let me know what you find and then we can proceed further.