When the load goes up so will the voltage - Honeywell Hw2000i Inverter Generator 125cc - In Box - Wow

Note the wiring diagram, the relay has to be energized before the fuse will get voltage. The load side of relay is that line with arrow head, when the relay is energized that line moves to other terminal and voltage goes to the fuse. Voltage to load side of relay is hot all the time. The control side of relay is left side in the diagram, has to have voltage and ground. Ground is a constant ground, voltage comes from bcm. Your neutral switch is part of this.

under-hood fuse block. fuse 16--20amp, that voltage goes to load/switch side of fuel pump relay. There is also voltage that goes to coil/control side of relay, that is 2 amp fuse, interior fuse box comes from pcm relay.
There is also a bump switch that you might need to check. Your owners manual should have this info.

In normal house wiring, 110 vac, the black lead is considered the "hot" or line lead and the white one as the neutral. When wiring to a variable resistor, the variable lead normally goes to the load so the voltage can be changed and the other lead to the "line."

Check battery connections. Check voltage at fuse panel. Should have same voltage as battery. If voltage is present turn on any switch, if voltage goes away with a load follow the no voltage procedure but leave the switch on while testing.
If no voltage, check for any fuses or circuit breakers in the supply wires. Still no voltage: connect voltmeter red lead to positive at battery, black voltmeter lead to negative at fuse panel. Voltage OK problem is with positive supply to panel. If no voltage connect meter red lead to positive at fuse panel, meter black lead to negative at battery. Voltage OK problem is with the negative supply to panel.
If fuse panel is supplied voltage from the ignition switch start the voltage tests at the ignition switch.
Sometimes the positive and negative supply for the fuse panel are connected at the engine. Usually the positive at the starter solenoid, if so use that source instead of the positive battery post. Voltage must be traced from the root source to the load. Both positive and negative must be isolated and verified separately. Without one, positive or negative, there will be no voltage at the load. The load being whatever needs voltage applied to function, (light, pump, etc.)
If there is a corroded connection or wire it is possible for voltage to pass through the corrosion with no load. When a load is applied more amperage is required. The corrosion is not a good enough conductor to carry the required amperage and the voltage goes away. This corrosion can be at a terminal connection, (wire to switch, battery cable to battery lug, battery lug to battery post, etc.), internally in a switch, wire, fuse or circuit breaker. It is possible for a wire to appear to be in good condition. The outer insulation can be intact while the inner conductor is corroded, sometimes turned to green powder. This is why marine grade wire is more expensive than standard wire. Marine grade wire is tinned copper, copper conductor electro coated with tin to resist corrosion.

check if this is a power wire or earthing wire, do a continuity test , one to chassis ,one to power , if get no continuity then the wire has a break in it somewhere

The AVR automatic voltage regulator normally gets damaged by a short in the rotor, wiring etc. MOST common is shutting the generator down under load and NO NO. The AVR goes wide open to try and maintain voltage on a gen that is stopping, always disconnect loads then shut off

either the board or something connected to the board is drawing a load or creating a no load situation, if the area the voltage goes to opens up the voltage will go up .

If you are a gambler replace the power board and find out.

Possible that the inlet valve is faulty. please measure the voltage on the inlet when the washer is switched on , if there is no voltage then the controller is faulty. If voltage is present then the inlet valve has failed.

bad voltage regulator most likely, that's a pretty small generator and a 500 watt load may cause it to work too hard, but it shouldn't vary that much in voltage