Immobiliser bypass

It will be possible but you are going to have to take a closer look at all the wiring.  You'll need to identify where the car loom is split by the immobiliser and then either remove it completely and join the wiring up or just effectively short it out.
 
So you need either a wiring diagram or you just have to get stuck in and identity all the wiring going to it, shouldn't be hard at all though.

Lets have a look then.
 
Is this a factory fitted item or aftermarket?  

Ah yeah, you will need to get a lot more personal with the car than that.  Probably be easier if you remove the lower part of the dash on the drivers side rather then getting your head up underneath it, you need to find the control unit and trace the wires where it splices into the cars loom.

It won't be difficult, easy money for someone!