With a headlamp designed to work with a hub generator (i.e. with a manual or automatic switch), is the tail lamp connected to the headlamp output working in series or in parallel ?
I thought the only reason not to connect the tail lamp directly to the generator (so in parallel) was to benefit from the on/off switch in the headlamp.
With bottle dynamos, I always connect the headlamp and tail lamp in parallel, three of the family bikes still have this setup.
Well, you would mount two filament lamps, 6V each, in parallel. You would also mount in parallel two LED lamps, one 6V, one a lesser voltage but with a built-in circuit to reduce 6V form the generator to whatever voltage the LED requires.
In each case it depends on what protection circuit for the lamp is already in place.
The advantage of a series connection, if the voltages of the LEDs add up to generator voltage, is that no energy is wasted in heating dropper components. But, if there are other circuits already built into the lamps to control the voltages, then parallel connection would work best.
At bicycle voltages/current you are unlikely to do much damage if you get it wrong.