As promised in the comments to my answer, I went out and measured the effect in a number of different configurations (a couple of days later than promised :-)). For those of you who just want the conclusions, here they are:
The remote seems to work better when held to the head though the improvement isn't as marked as one might have expected from a google search of the topic. The best possible orientation seems to be to hold the remote flat against your temple. If you aren't willing to hold it to your head, pointing it at the vehicle seems to work better than pointing it up, and there doesn't seem to be much dependence on how high you hold it. Finally, holding the remote to your chest is worse than just holding it at arm's length.
The Experiment
I chose six different positions in which to hold the remote, and in each of those positions I held the remote in two different orientations (described in the list below). 441
In each position/orientation I clicked the remote 3 times, waiting a few seconds between clicks. I recorded the number of times out of 3 that the car responded to my click.
The car, a 2009 Volkswagen GTI, was parked sideways. Temperature: 70.5$^\circ$ F; Barometric Pressure: 29.75 inHg; Humidity 86%; Winds: ~5 mph. There were no large structures around accept for the concrete encased stainless steel vacuum tube of the LIGO Livingston Interferometer which runs parallel to the measurement axis and extends for kilometers in both directions. The battery in my remote is a bit old, but I tried to keep my clicks evenly spaced and began with several discarded clicks to try and cancel out battery effects.
The different orientations are documented in the picture below, but here is a description
* Low (Foward/Up): Held down by my leg pointing the remote towards the vehicle or pointing it directly up into the sky.
* Middle (Forward/Up): Held my arm extended to the right pointing the remote towards the vehicle or pointing it directly up into the sky.
* High (Forward/Up): Held my arm high above my head pointing the remote towards the vehicle or pointing it directly up into the sky.
* Chin (Pointed/Flat): Held against my chin either pointed up into my chin or flat against my chin.
* Temple (Pointed/Flat): Held against my temple either pointed into the temple (like a salute) or held flat against my temple.
* Chest (Pointed/Flat): Held at the center of my chest pointed towards my chest or held flat against it with the remote pointing up.
The Results
In table form:
and graphically: 441