Ahh. Misunderstood. Lamp is coming on when it should not be! I thought is was with hi beam on.
Since that indicator lamp is wired across the high beam filament itself, there may be a leak to the high beam wire.
That circuit is pretty much isolated, it comes from the hi/lo switch which gets power from the lighting switch then goes directly to the headlight connector plus the indicator. So the leakage must be inside the switchpod I think, maybe in the switchpod harness if the wire insulation is damaged.
I suppose it could also be a strange ground fault in the indicator assembly (or speedo, you don't say what bike you have). Some indicators get switched power (hi beam, signals), some switched ground (neutral, oil pressure).
A low voltage will dimly light the tiny indicator bulb but barely warm up the headlight filament. If you have an LED indicator it will light dimly with miniscule current once the voltage gets to its Vf, usually 2 or 3 volts. That can happen when converting to LED lamps, tiny leakage that doesn't light the original one now gives a dim glow. Neutral switches and brake light switches sometimes do this.