Power Supply Prematurely Off
Measure the cold resistance of the bulbs. You’ll find that it is much lower than the wattage would imply. Incandescent filaments have a much lower cold resistance that increases as they warm up. This means that your 4.6 amp bulb will probably draw well over 10 amps at startup. Your power supply can probably supply additional surge amperage at startup but not enough for two bulbs and it’s going into overcurrent shutdown.

Your power supply is probably just fine.