Simulating a click without using the mouse at all

Hello,
i am interested to know whether it's possible to simulate a left mouse click without using the mouse at all.Note,that i am not saying without moving the cursor.
The reason behind my question is that with ControlClick the mouse must be present/captured,but i want to run my script on a remote server - VPS - so there is no mouse until i am logged in.After that,you know,the the physical mouse on my computer can be used in the remote desktop as well,so the script works flawlessly,but when i am not logged in,it can't be executed.Actually,it hangs on the very first click that must be simulated ...

Any workaround/solution will be greatly appreciated!