Hi @jonthommarson,
Did you check with a voltmeter or a test lamp whether the power is getting to the lights? Not sure as you just said that the fuse and relay seemed OK. Also check that there's a good earth connection for the lights.
Here's an image from the Honda Odyssey 2006-2009 repair manual showing the wiring diagram for the backup lights.
Hopefully it is the same for the 2005 model.
[image|3146617]
(click on image)