Any bulb that is the same type as OEM but claims to be brighter than the stock bulb will always burn out sooner. The brighter the aftermarket bulb, the shorter the life.
The statement about the Goldwing second headlight burning out because the first one went bad would seem to be BS unless there is something else going on in the lighting system that this non Goldwinger doesn't know about.
The headlight relay can't cause the headlight to burn out, with one exception to be discussed later.
The most important piece of information is that the voltage is normal. (Under 14.6 volts, right?) If this is true, then you will need to be looking at the items that follow.
The remaining reasons that can cause a headlight to burn out early are excess heat, vibration and power switching.
* Heat would be caused by a non-stock bulb or modification to the stock headlight bucket.
* Vibration can indeed be wheelies, as well as super rough road surface or dirt roads. The prospect that this is related to the early burn-out is remote.
* The other thing that can get to a bulb quickly is power switching. One of the toughest things a bulb has to deal with is power being turned off and on. DOT approved headlight modulators have very specific rates that they can cycle, and a very specific power level that they can not drop below when the modulator reduces power. This is done to prevent thermal expansion/contraction damage to the filament. If the modulator were to turn the bulb fully 100% OFF and 100% ON the bulb will die very fast. This is the background leading back to the headlight relay. If you have an intermittent electrical problem with the wiring harness, headlight socket or headlight relay that lets the bulbs flicker, it will kill the bulbs PDQ. Right now, based on the given information and your rapid bulb failure occurring to stock bulbs, I think that you should be looking into an intermittent electrical problem that is causing the bulbs to flicker. Disclaimer: Remote troubleshooting can only be as good as the information supplied.
Edited to add: It is very normal for the R & L low beams to burn out at almost the same time. It is not normal for them to burn out again in a couple of weeks. Some people will change one of the two replacement bulbs ~ 6 months later even though it is still good, so that when one bulb dies a natural death, the other bulb will still have 6 months to go and not leave you in the dark, late at night, far from home.
After re-reading your initial post, perhaps you are simply a victim of 'just one of those things', a one time coincidence that will never happen again.