The entire body an engine is GROUND. To check a ground wire you check for continuity from the open end of the wire to ANY bare meta on the car.=l.

 

I know any bare metal is ground, obviously the metal is all touching :p I'm just trying to follow instructions here, making sure this ground nut is secure and connected, and part of the wire is not frayed, so, what's next?
Finding and cleaning and checking G105 was pretty rough on me, that was like - what I did today, considering the state i'm in, whew! But important to see the whole circuit, I understand.

The whole circuit seems complete. I'm not sure where the fault is, I can only think that... I have not checked to see that the relay is properly recieving the signal to switch on. The relay itself has been tested while unplugged for clicking , connecting, and breaking connection.
I mentioned earlier I found live 12v at the relay, but i think just on the one pin that is constant 12v batt. Hm, so if the fan is not coming on, the relay must not be switching on. what's the best way to test this? Would I have to have the relay partially popped up to touch the pins while they are inserted?

 

also i apologise if you misunderstood why I was asking earlier - I think it is super important to go into not-very-familiar territory not assuming i know everything, and also ensuring I am using my meter correctly, get it right the first time, you know? :) making sure there is not a ground connection test i'm not aware of.
To confirm, the meter is supposed to read like that in the video right? This is the first time I've actually used that setting, despite lots of past electrical tinkering.
Super appreciate everyone's help thus far! Nearly everything is ruled out, got to be close now.

 

Determined to figure this out, here are how the four relay pins are behaving at temp. the right two are completing a12v circuit with ground through the meter, the left lower one has ground continuity, the left upper one has neither. Is that how it's supposed to look at temp?

 

The diagram you posted in #23 tells you everything you need to know about the relay. There should be a diagram on the relay showing which pin is which, or numbers on the pins. If not GoOgle "4 pin relay" for images or, just probe the socket
Easiest way to check the fan circuit is to jump pin 30 to pin 87 in the socket, the fan should run. Pin 30 and 85 should be hot at all times. Pin 86 should be ground when the fan is supposed to ne running. To test for a click jump 86 to ground and 85 to 12v.

The pin numbers on relays are standard. The orientation of a 4 pin relay does not matter.

 

Thanks! I previously read a thread where you explained to a mechanic how these could be swapped both ways and he disassembled it to confirm, "these new fangled things are tough on us old mechanics" good edicational thread. I had searched google but did not find anyone checking the socket directly, did not think to simply jump them, excellent troubleshooting experience. Thank you my friend. I'm used to doing technical stuff with bacteria and petridishes not electronics, patience appreciated.

Jumping relay pin 86 to ground and relay pin 85 to 12v: Click!

For clarity/reference I have the relay turned at this orientation.
85 87

30 86

Engine turned on:
Jumping 30 to 87: fan turns on!
(upper left socket) is not hot, no ground continuity either just to provide that data for you.
(lower left socket) is not hot, it does have ground continuity.
(Upper right socket) is hot!
(Lower right socket) is hot!
So obviously, the way it's built to work both ways, if I rotate the relay, 30 and 85 as marked on the relay case will plug into the sockets reading hot, but the fan still does not come on.
It's reading same as the 4x meter image I posted earlier, that is the data I have re-confirmed. Do you see a problem anywhere? Scratching my head here...

I feel like the only thing I have not gotten a visual on is whatever is under the relay socket case. I tightened those bolts really tight tight tight.
Everything seems right. now we know the cable leading to the plug works. Is it simply not getting the signal to click on?

this suggests my coolant sensor could be starting to fail, those are my symptoms exactly. at 1:37

 

Okay, so in the current orientation:
86 and 87 are hot, getting power through the fuse.
30 goes to the fan. (Light blue wire)
85 goes to the ECM. (Dark green wire)

When coolant reaches 219 degrees, or the AC compressor turns on, the ECM is supposed to complete the circuit to ground, which closes the switch inside the relay, sending power to the fan.

So it seems that there are a few possibilities
1. Something wrong with the Dark green wire.
2. Something wrong with the ECM.
3. Whatever data the ECM uses is not reaching the ECM(Engine coolant temperature sensor? )
4. Anybody else have any ides?

 

Just noticed the video. Do you have any of the other symptoms? CEL on?

 

DC electromagnets don't care which end is + and -. switches don't care which is in or out. 4 pin relays can only be installed one of 2 ways, either way is ok. The pins are arranged so that you can't plug it in wrong!

 

donbrew only had to beat me with a baseball bat a few times, but he is correct. relay can go in place either way and it should work. I found the connector at the fan was intermittent and I spliced it directly, bypassing the connector to fix my fan not working. I have learned that when these guys tell you something, they are 99.9% correct.