The tail lamp has no bulb; the headlamp has a bulb and works great.
back to the basics ... load : 6v, 3w. typical split, 2.4w headlight, + a 0.6w taillight..
[NB: voltage is the same, it's the wattage that is higher front/back,
once shared load is reduced , the remaining filament gets all the power, so overheats]
screw base headlight bulbs^ seem to be quite sparsely available of late.