False oil light preventing start up

Afternoon all, I have fitted Oxford heated grips by wiring them in to the LHS side light in parallel (to prevent me from flattening the battery again by leaving them on whilst parked up). I have also replaced the clip together joints of the heated grips with soldering joints (as occasionally water ingress in these was causing the grips to cut out sporadically). The grips work fine now, however, the bike doesn’t start!

The bike make the correct sounds on starting up (including that little whir when moving key to the on position), the lights and other electrics (including the LHS sidelight and grips) all seem to work. It shows the oil idiot light and also the oil can on the LCD bit of the screen. I know that some of the idiot lights usually show on start up, before it actually starts, so this may well be a red herring, but I can’t remember exactly which ones it shows. When I press the starter, nothing happens. I’ve checked the obvious, in neutral, sidestand up, clutch in, kill switch in correct position. I’ve also tried disconnecting the batter for a couple of minutes (which has solved a similar problem with the immobiliser in the past), to no avail.

The bike is an SV650S K4. Aside from the heated grips, the only other modifications to the wiring loom are a tomtom charging cradle wired in on parallel on the RHS sidelight and an immobiliser, both of which have worked for months/years without fault.

Short of disconnecting the heated grips (which I’d rather not as the grips themselves are now glued on, throttle tube cut down to accommodate them, etc), is there anything else I can try?

TIA,

Ceri

[northwind]

Oil light's normal, the oil pump is mechanical so there's never oil pressure when the engine's not turning. It doesn't even click when you press the starter? I'd usually suspect a flat battery but I don't know if the FI pump would work if that was the case, so I'll hedge my bets and say maybe it's a cutout switch, specifically, maybe it's the clutch as you'll maybe have been working in that area and it's surprisingly easy to bump.

Or, it's the ****ing immobiliser. But I have nothing constructive to say on that

Just had mine out for cleaning, so I can fill you in on which ones come on normally - Red fault light (left of speedo) and Fuel low light (on solid, briefly).

None of the things in the speedo itself come on after the initial test (where everything lights up). If there's a fault, it would come up with CHEC next to the temp gauge, so if that isn't showing, I'd reckon on a cutoff switch (not the master on the right bar though, as the FI doesn't charge if thats off)