Off hand, any two lights that are drawing from a single power source will draw different current.

It is likely that the tail light would draw more current. If you need to run the lights for a short period it's probably no big deal. But as the battery drains, the head light will dim first unless for some reason the Dinottee regulating circuit produces more resistance than the Lupine head lamp. (unlikely)

Supposing both lamps have dual value regulating circuits you could have unexpected results. By the way, my old Dinottee lights do more than a simple "cut off" at 6V. The actually maintain a near constant wattage across a range of values.