With a little calculation and an estimate.. A normal interior bulb takes about an amp. That makes 12 watts at nomimal 12 volts. Likely a faint glow would be only one watt.
What happens? Well, instead of having a single bulb getting power through the filament to negative ground, power is not finding it's way back on the ground. Power then goes out and finds it's way back through another filament. You still have 12 volts in the circuit, but voltage drop to produce one watt would be around 3.5 volts at that bulb, and the other 8.5 volts is dropped somewhere else.
As others have said, you need to not only provide power, but also be sure every ground and negative return is connected.
