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Usually bulb circuit faults are not caused by a completely open circuit, but instead by just a few ohms of resistance. But since you are starting off with only 12 volts, it doesn't take very much resistance to reduce the voltage so low that it won't fire the bulb, and the more current that you draw, the more voltage drop there will be.
Don't be fooled, however, when you connect a voltmeter (remember, a voltmeter is, and
has to be, a high-resistance device, so it draws almost no current) across the
unloaded circuit (i.e., bulb removed) and you get almost full battery voltage. This does not mean the circuit is good, but instead merely that the relatively low resistance in the circuit causes
almost no voltage drop because so little current is being drawn through your voltmeter.
But when you
load the circuit (insert the bulb) and connect your voltmeter across the circuit again, there will significant voltage drop because substantial current is being drawn. This is the dead giveaway that you need to chase down the bad connection.