On-- off-- on-- off timer circuit
Based on your need for arbitrary on and off times and a small fixed cycle, as well as low current, then as mentioned in the comments, a micro controller will do what you need with minimal code.

Pseudo code

While(1){
    sleep;
}

Interrupt on input high to low{
    output on;
    wait 1000ms;
    output off;
    wait 1500ms;
    output on;
    wait 1000ms;
    output off;
}