Since the tailight is "plug and play", I would assume that the light has a built in load equalizer, so that should not be an issue. Even if it does not have a load equalizer, it wouldn't cause issues like a non-start. If anything, the bike's system would "see" the tailight as a burned out bulb since it draws a lot less current than a regular bulb.
I would make sure you have a good battery, especially if it is the original and has not been continuously maintained on a Battery Tender when parked at home. 5 years on a battery is pretty good service, IMO. Low voltage can cause all sorts of electronic gremlins to show themselves.
A fully charged battery, with no load connected to it, should show a minimum of 12.6 volts...anything less is partially discharged. Disconnect all the wires going to the battery terminals and measure with a digital voltmeter. If less than 12.6, hook a battery tender up and charge overnight and measure again to see if the battery will take a 100% charge. If not, get a new battery. Also, be mindful of the fact that the '06 model year had some bad batches of voltage regulators installed...mine had to be replaced, but it was during the warranty period. You have a 50 Amp alternator in the '06, so it should be fairly easy to add up the total amps pulled by whatever you've added, plus the needs of the bike with no additional add-ons, to calculate whether you are exceeding the output of the alternator.
If you get a new battery, install a SAE pigtail on the terminals and run the connector to a place under, and in front of, the battery box with a wire tie. EVERY time you park the bike at home, hook up a battery tender...the bike pulls current from the battery, even when parked...not much, but some.