You could be using leds or a compact fluoro for this. These will be for use with a 12V battery. It may be you want to reconsider using 40W, as less power is much more feasible. About 10W of CFL or LED supply will be the same as a 40W incandescant lamp, and last much longer.
If using leds you will need an efficient switch mode current regulated source to drive them. You can expect similar efficiency to a compact fluorescent lamp. The leds will need heatsinks.
The size of the battery and the panel are critical parts of the design. The power supply would be a 12V battery. The light runs at night only. WIth some care the solar panel itself can be used as a sensor to switch on the lights by measuring the battery voltage. When under charge it will be around 13.85V, using a float charger. The current is inherently limited by the panel.
A simple but effective charger is to connect the solar panel by a switch (P channel mosfet as a high side switch or relay) when the voltage is below 13 volts and disconnect it when the voltage approaches 14V (lead acid battery). Use a reverse blocking diode with the panel. Note that gel type batteries are not very suitable for operation in sunlight in the tropics at least. When the battery is below 12.6V consider it as night time. Otherwise use a separate sensor for sunlight. Thus you have three voltage comparators for these 3 voltages. These can be a schmidt trigger with the correct hysteresis. You need a reference supply. A small 5V regulator is simple.
This uses a solar panel designed for charging a 12V battery, meaning it has 36 cells. The OC voltage at standard conditions is 22V. Look up data sheets specs for panels.
If the lamp runs 12h per day, and the power is 10W, then it uses 120Wh per day. With a 12V system this is 10Ah. The battery needs to be at least 10Ah, especially considering overcast days, and the need to not discharge it below 50% of capacity. This looks like a 40Ah battery therefore. The maximum charge rate should not exceed 4A (10h rate).
The solar panels must provide 10Ah per day too, but...
The battery takes 140% of its discharge to recharge, so now 14Ah per day.
Allow extra to catch up after a period of overcast weather, at least 20Ah per day.
The rated current occurs with full sun. There is an equivalent of full sun hours for your region, likely 2-5h a day. In the tropics 5h per day. Thus we need 20Ah in 5 hours, so a current of 4A. This agrees nicely with a 40Ah battery.
So for a 10W lamp operating 12h a day in the tropics we need something like a 40Ah battery, and a 4 amp x 36 cell panel. This will be rated around 15V * 4A = 60W. A bigger panel is ok within reason, but should have a bigger battery so it doesn't charge too quickly. A bigger battery may be needed to increase the lifetime, and allow a reasonable number of days without sun if overcast weather lasts more than a day or too. The electronics should all be designed for outdoor use, vermin proof, including rats to ants, weather-proof and able to operate at 60°C ambient temperature.
The link below has an example of a P channel mosfet high side switch driven by a voltage comparator. Use a 10A or more rated switch and the comparator needs a reference so it turns on at 14V and off at 13V.