As stated above, the FZ has a max charge of 14 volts at 5,000RPM.
It still is charging under that, just not as much. At idle, your probably at a loss(draining your battery) with the second light turned on.
You can put a voltmeter across the terminals and see what the voltage is when turning on the lights/accessories, etc. If its right at 12 volts, your running off the battery. Rev the engine up some taking note of the voltage. If your above that, the charging system is charging, just not at full capacity until 5,000 RPM's.
I plugged in a heated vest and heated gloves (Widder) in the BMW outlet I have installed on the left side of the bike. As long as your above a certain RPM, I can run the vest/gloves while still CHARGING THE BATTERY (above 12 volts). If stopped at a red light, I turn off the vest/gloves. As a side note, I can do the same with my KLR 250 which has an even smaller battery (kick start).
I've had the BD43 installed for probably a year and a half and run high and low beams on during the day ALL THE TIME. I haven't had a problem with the charging system/battery however it does sit on a BMW automatic charger when not in use and doesn't get ridden in stop and go traffic everyday. I keep my idle set at 1,000, yes, it's below the recomended 1250-1350 RPM.
If your in stop and go traffic everyday and at low RPM's, I'd probably turn off the high beam and make sure the idle is at the specified 1250-1350 RPM for charging purposes.
BTW, I bought my bike from from the original owner (my friend) who had the OEM battery fail two days after taking delivery. The shop replaced it under warranty, been fine ever since. You may want to get that battery load tested as it could be bad(dealers turn the bikes on and off on the showroom floor, start it for a minute), which kill the battery. This scenerio is very likely for your bike....
Scott