NOTES:
1. R2 limits current spikes to Q1.
2. R3 limits current flowing through Q1c-e.
3. Bulb resistance measured when cold.
4. Total Darkness* current measurements:
5. Q2c-e / bulb I=172.3mA
6. Q1c-e / Q2b I=9.8mA
7. Q1b I=55.3uA
8. Total circuit leakage current in daylight and twilight: I=62.1uA.
9. Try substituting other NPN transistors for Q1 & Q2; just about any should work fine.
Q2 is a power transistor more than capable enough to handle the 170mA flowing through its c-e junction once it is turned on. Current flows from the input through Q2c-e through the light bulb to ground, turning on the light bulb.
At night, the total circuit drain is about 182mA, which should keep the light going for about 5.5 hours after sunset.
With a larger solar panel array, or supplemental charging from a generator during the day, the nightlight should stay on until dawn even with a 75% charge (winter) or 60% charge (summer).