Hi,
There is no brown-white wire going to the alt. It's blue-wite.
The fuel pump draws a ludicrous amount of power - much more than can ever be supplied by a sneak current.
The ECU itself won't spark the plugs on a sneak current.
The injectors won't open on sneak current.
Anyways, that means that it can't keep running for long because the fuel pump cuts out so the most it can do is a second or so on the remaining pressure in the rail. And if it does that, it means that something in the combustion chamber(s) is *glowing*, igniting the fuel.
This is either a sticky fuel pump relais or some carbon or the prong or electrode on the plug. The latter can be caused by low octane fuel because detonation destroys the boundary layer that prevents direct contact of the flame front with the metal in the cilinder.
So - you check the plugs, put in some decent fuel and a bottle of STP Complete Fuel System Cleaner (solver bottle, don't waste your money on anything else)
If the problem remains, you replace the fuel pump relais.
Manfred