Here is the link to the device:
AS-10-12

According to the instruction, The input must be 12-volt ac OR dc
But the output is what? is it 12-volt ( dc )?
If I want to provide 240-volt as output I must use EXTERNAL source; I guess!!!!
The other logic is :
The relay inside the module is providing switch capability; ie is does not provide any output ( N/O, N/C )
Help is needed to test what voltage is required and how to connect a 240-volt lamp as a load

 

First, that link is to a seller that knows nothing about the product except price, weight, and shipping cost. So the seller is of no help.
What I do see is in the second photo the tag listing the applications. The only voltages shown are 12 volts.
A standard rule is that applications not listed are not intended, and that capabilities not claimed are not promised.
This device is ONLY suitable for use on 12 volt circuits. I would expect that the application of mains voltages, either 120 or 240, will result in immediate destruction, possibly with actual fire.
Mains voltage rated products are available that are rated for the specific voltages and currents and are UL rated for safety and fire resistance, and they do not cost that much more than this unsafe product.

 

Totally agree with your assessment.
This will work with a load of 12 volts ONLY.

 

But the ad does say that different Voltage Rated versions are available.
BTW, there is NO-RELAY inside this device,
it is a "Bi-Metallic-Switch", with a Heating-Element,
the Current of which is controlled by a LDR, ( Light-Dependent-Resistor ),
just like they've been making them for at least ~80-Years.
.
.
.