Although the EWS used to be a common problem, the instrument panel will light up regardless of whether it was working or not, it would simply show a EWS fault in the instrument cluster. Also this is the same fault that would show if your bike 'forgot' the key.
The problem you are having will be with the switch side of the igntion barrel not the immobiliser side.
More then likely it will be the wiring around the top yoke leading to your barrel, the switches are pretty bulletproof now days.
If you look at the back of the ignition barrel(towards the front of the bike) youll see a black cover covering the EWS module take this off, youll need a small torx tool, t8 if i remember rightly, after taking this youll see 2 connections, 1 right in front of you which is for the EWS ring and 1 hidden a few mm back, this is the one you need. Although you cant see the connector all you need to do is give it tug on the wire to pull it out.
start stripping the fabric tape back from the connector, if you do this right you wont reveal any of the metal wiring just the outer sheath for the wires, keep stripping it back and they normally break where they are cable tied to the frame just below the headstock.
if you cant find the break then it might not have broken the outer plastic sheath of the wire in which case will need a multimeter to find the break.
also if you cant see it what you could do is plug it back in to the switch, turn the igniton switch on and wiggle parts of the wire between two hands slowly moving down the wire until the igntion turns off.
Im not syaing this is exactly what the problem will be, that i cant say unless testing it myself, but i am pretty certain of it.
Also if this is the problem it will not show on any diagnostics machine as all the bike thinks is the igniton is switched off which is a normal state and wont show a fault. Finally again if this is the problem then it will get worse with time causing the bike to potentially turn off whilst riding or just not start to begin with at all.
Hope all this helps