Flickering lights and lights that get brighter than normal.... Doesn't this scream "Loose Neutral"? A loose neutral can sometimes cause the voltage on certain circuits to rise above normal, while at the same time the voltage on other circuits will fall. That is not a good thing.

The problem is upstream. Check the other receps on the circuit for a bad connection. Plug a table lamp that you have turned on into the non working recep. Then, while someone watches the lamp, go around an plug something into each upstream recep and wiggle it around. When the table lamp flickers, you have found your bad connection. It will most likely be the neutral(white). Another possibility is a GFCI that you think is reset but it is not. The ones with the black and red buttons do not always reset easily, sometimes not at all. Since this is an outdoor recep, depending on when your house was built, it should be on a gfci, maybe the one in the bathroom? And a third possibility, are you sure the recep is not switched? Your test results indicate an open neutral, could be caused by any of the above (including a switched neutral).

I have the exact same issue but performed a few different troubleshooting steps that were not mentioned here. To begin, this is a rental home built in 1972. All aluminum wiring with some copper for lighting overhead that was updated in 2009. My washer is brand new, LG high efficiency & overpriced. I’ll add that I have a matching oversized LG gas dryer too. They both plug into 1 receptacle with the a top and bottom outlet. This is wired back to the breaker box as 2 20 amp circuits. They share a neutral wire. The circuit breakers were old and not joined with any bar that physically connected the two switches into one so that one off makes both off. The receptacle was old, loose and burnt up some. And even more concerning, the tab on the line (right side) was not broken to properly separate the top and bottom circuits. Luckily I didn’t find out the hard way. Although the panel was not labeled/correctly, I went through process of elimination by turning everything off and then testing one breaker one at a time and matched to outlet(s)& lighting it controlled. I assume that someone replaced this laundry receptacle at least once in the distant past and forgot to break the right tab. I replaced the receptacle with a new 20 amp outlet and broke the tab on the right side only. There is a red & black wire (on right with tab connecting top to bottom removed) and one shared neutral wire that is white (on left with tab intact.). It is also grounded of course. I also replaced the two circuit breakers in the box with new and specifically for this type of setup. It has the bar that physically joins the switches for off and on. I also checked and tightened all neutrals in the panel. But even after all that, the damn dimming still occurs when agitating. I should add that all my lighting is LED too. Here is the last important clue that I would think others could try too. I was doing some laundry and it had just started to agitate and dim like always. Just as a temporary measure, I paused the cycle & then hooked my washer up with an extension cord to another nearby circuit. It’s about ten feet away and it’s a heavy duty cord but was my last straw of an idea to check & was not a permanent arrangement. Anyways, the washing machine worked fine and there was no dimming throughout the entire cycle. I left it like that for a few days and it continued to perform without dimming the lights. Additionally, this dimming would occur whether the dryer was also being used or when it was off. Keep in mind that they share one neutral. I tested both the top and bottom outlets and the readings all indicate a grounded correct setup. There is no open neutral. I still don’t know why it does this but believe it is definitely related to wiring, not machine. Perhaps i also need power company to come out like person above had when their issue was resolved. I’m moving to purchased home in a matter of weeks so the landlord can decide how to proceed from here. just to give you an idea of the mess this was....

(and are switched!) I love switched outlets, but I wouldn't want them ALL to be switched. We have amazing recharging batteries these days, and lamps can't be such a huge power draw. Why do we even HAVE outlets anymore? You're right that lamps aren't a huge power draw; my husband, who is an engineer in the energy industry, says that only things that produce heat are real energy-hogs. Your TV, radio, lamp can run all day for pennies. However, I disagree with your conclusion. Batteries are great, but they're more trouble than things that're plugged into the wall. They do run out of juice (at the least convenient times) and they do have a lifespan (for example, my laptop will no longer run at all unless it's plugged into the wall -- the battery cannot hold a charge anymore, and a new battery costs $140). but once a room is furnished they are mostly ignored visually, anyway. Good point. Outlets at foot-level are easier to ignore than outlets at eye level. In reality, I suppose both spots have their uses. You probably haven't touched -- in years -- the outlet into which your bedside lamps are plugged, but you touch your kitchen outlets and the outlet where you recharge your phone daily.