My old washing machine had a water level selector so you could do very small loads and not waste excess water. My new LG top loader says it has a load sensor but I wanted to launder mop pads which ar

Question 2 also edited for clarity, 'LG' not 'lg'.
No model details again.

Surely not during 'Rinse' cycle? That just adds water and gently tumbles to get the soap out and complete the washing by further agitating the clothes. You must mean during spinning and much depends on if it is a front loader, or a top loader. For both, machine not level front to back and left to right and / or not sitting firmly on all 4 feet.

Top loader, bulky load unevenly loaded.

Front loader, single bulky item causing an uneven load.

You just need to find where from?

Back of the soap dispenser.
Water Level Sensor.
Hoses under the drum.
Drain Pump.
Drain Hose.
Door Gasket on a Front Loader.

Full 'make model top load / front load' is useful in these questions

https://www.google.com/search?q=LG+washing+machine+leaks+when+filling

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When I was looking for a new washer, I looked at front loaders and was told that they are not really for dirty clothes, it is more for sprucing up an outfit or shirt. They are supposed to be energy efficient read this less water and shorter wash cycle.
I would go for a top load heavy duty, stainless steel tub.
You are just wasting money trying to get this one to wash over and over again. good luck.

You have not share what is the year, make, and model, but many washers have this feature I will tell you of:
On the control panel is a rotary dial telling the machine how much load you are going to put in the machine, hence how much water you wish the machine to have in it for the clothes.
That switch has a clear plastic pipe, small diameter, that runs from the back of the control down to the bottom of the wash tank.
As the water level rises, the water pushes air up inside the pipe to the switch, which shuts off the electricity when the proper water level is reached.
Rodents, old age, and excessive movement can damage the plastic pipe, causing the machine to overfill.
God bless your efforts.

You cant, water levels are factory set for optimum water efficiency, new machines use a lot less water than older machines, poor wash results are usually caused by over loading

YOUR WATER LEVEL SELECTOR ( SMALL-MEDIUM-LARGE)

If the cycle does not stop draining that is usually because of a faulty membrane switch that controls the water level in your appliance.
The faulty sensor cause the machine to think that there is still water inside, even when water has drained completely.

I had a similar problem. We has placed the waste water hose into an old tub next the machine. The plug hole int he sink has become blocked with lint. When the washing maching was pumping water into the tub, the tub would fill with water, which would rise a level higher than the washing machine waste hose. What this appeared to do was cause the machine not to be able to properly pump out water, leaving this horrible back stuff in the wash which would end up all over the wash. Ensuring the plub hole in the tub was clear solved the problem immediately!

There are easy checks before you replace the level selector body

remove the trim plates at both ends of the control panel to expose Phillips head screws 1 at each end. remove the screws
lift and swing the control panel up and over the back, it is hinged at the top.
The washer can be operated in this condition for testing

1 Rremove the air hose, and blow it out.
often water remains in the tube after changing levels, the water is not compressible so a small change in water level in the tank, makes too much difference in the sensor.
reconnect the tube and try a cycle ~1/3 chance of fixing it

If fail,
2 The spring inside Kenmore water level sensors that reacts to air pressure in the tube is not up to the job and stretches, not noticeable till changing water level settings moves the anchor point of the spring.
pull off water level knob from control panel front, from control panel back depress lock tab at right of level selector body rotate counter clockwise 45 deg and remove
adjacent to selector knob shaft is 1/8inch nut, turn clockwise to raise water level counter-clockwise to lower water level, test, adjust, test adjust ~1/2chance of fixing it

If fail
replace level selector body