If the receiver has a relay, I would wait to connect the motor until I hear the relay clicking. Then, I would use a tester to identify the contacts.
You should read the instruction manual of the transmitter+receiver.
Most likely, you need to "teach" the receiver which remotes are allotted to communicate, and the button on the receiver serves that purpose: try to transmit while the button is depressed, or, try to keep it depressed a few second to enter learning mode (perhaps a LED starts blinking), or something like that (and that would be on the user manual...)
...AFTER THE COMMENT, SOME CLARIFICATION...
About the "wait to connect the motor":
It was just a thought about not connecting powerful items before knowing that the system is working as intended: less things are connected, less problems you have, you can explore the system with more comfort. But in this case is not really important.
About "the tester":
Sorry, a misnomer. In my language, a tester is a multimeter. Used in "continuity" (ohm) you can identify the contacts of a relay without breaking anything. Another precaution that, in your case, could be a little too much.
I looked at "similar items" in the ebay page you linked in your question. Citing "technical data" from what I've found (https://www.ebay.com.au/itm/DC-12V-10A-433MHz-4CH-Wireless-Relay-RF-Remote-Control-Switch-Receiver-oPTUKT-Y1/402351163728)
Encoding type: learning code (1527)
...means to me that the receiver must learn the transmitter(s). There is a lot of 433 Mhz transmitters around, the receiver must respond only to the intended one(s), so you must indicate to the receiver what transmitter it should acknowledge. You do that by make the receiver listen to your transmitter ("learn procedure"). I don't know what the number 1527 means, but I think this is not important.
Match code way: fixed code
Radio remote controls use mostly two systems: "fixed code" and "rolling code". The fixed type is simple and easy to duplicate; the "rolling code" is hard if not impossible. Remote controls for cars use the "rolling code" system, because they have to be hard to duplicate. Essentially "fixed code" means: the remote sends, always, the same (fixed) sequence of bits. Typically there are 12/24/32 bits. You can "listen" to those bits and replicate the sequence at will - easy. "Rolling code" means that every time the remote sends a different sequence: you can listen to that sequence, but that one is already invalid because the next time, the receiver will accept only a different one than before.
Now, in the (uh...) "technical data", I've found this:
- Learning method: Press the learning code for 3 seconds. The indicator will be off, and then loosen your finger, press any button of the remote control to transmit signal, the indicator flash 3 times and then normally on which means you learn it successfully.
- Remove/clean method: Press the learning button about 8 seconds, the indicator will be from being off to on all the time, it means the information that you keep have been removed successfully.
If the procedure depicted above does not work, try to post a photo of your receiver, I will try to identify the model to find the correct procedure. Of course your receiver can be broken, but probably not.