What are the correct pinouts of this model of MAF sensor?

Hello, pins 1 and 6, so probably E and A there, pin 1 should be White/Violet wire and pin 6 Brown/White, those pins are for the intake air temperature sensor which is built into this MAF, I'll get the rest here for you in a couple minutes, I just want to verify theses wire colors for you. Let me know if those are correct so far. I'll post wiring diagrams as well.

Are you getting any specific trouble code stored? The voltage chart in diagram 2 doesn't list the Cougar, but being a 2liter it should be within the range of the these other 2liter engine vehicles when it comes to the Signal output, not sure why service info doesn't list more information, but if you find the sensor is bad, you can try cleaning it if it's a hot wire sensor and not a door type, you can buy MAF cleaner at an auto parts store. If the sensor needs to be replaced, diagrams 3,4 are to reset the KAM (Keep Alive Memory) to reset the fuel trims back to zero and the PCM will relearn the new sensors voltage inputs.
I'm going to keep looking for more information because Ford used a digital MAF in a lot of cases which varied the signal frequency to determine intake air flow.

https://www.2carpros.com/articles/mass-air-flow-service

https://www.2carpros.com/articles/how-to-replace-a-mass-air-flow-sensor-maf

There are a number of different MAF codes, so if you have one, we can look up that criteria.

This is the OEM manufacturer MAF wiring diagram and it is the same as the aftermarket redrawn one. So that's correct on wire colors. It looks like the PCM is just monitoring voltage for the MAF Signal, there is a Flow Chart for the MAF codes/diag, if you want that let me know.

Okay, glad to help, is it setting any specific codes?

Does your scan tool allow for engine computer live data? And does the Lpg run through the fuel injectors as well, or is that injected some other way? I haven't seen a Lpg vehicle in a long time, usually there is a conversion kit for fueling. I'm actually pretty curious to be honest. Are there two different setups installed?

Okay, so on these vehicles some of them have a Fuel Pump Driver Module that is separate from the PCM, it takes commands from the PCM, but it is in control of the fuel pump. It has 2 wires that run to the pump from the driver module and the module controls the pump pressure by varying the Duty Cycle of the pump (diagram 2) through the Driver module, so it might be that there is corrosion in the connector of the module, or an issue with the circuit board inside, you mentioned it happens more when cold, modules tend to act up when either hot or cold.

The diagrams below show how the Driver module controls the Fuel pump with that type of setup, on the 3rd diagram it shows the location of the Fuel Rail pressure test port. Ford uses a small port that you can screw a fuel pressure gauge onto and see if you are losing fuel pressure during this stalling out fault.

With no codes setting, I would check fuel pressure before you start the vehicle for the first time in the morning, if this is happening when the vehicle is cold. You should have a MAF code setting if it was the issue,
Most all basic fuel pressure kits have the small adapter for Fords fuel rails, here is a guide to help with pressure testing.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Service info states there is an Early and Late production for this year, the Later production has the fuel pump Driver module, so that explains why it's not there.

A mechanical gauge on the fuel rail will give you a much more accurate reading and will also tell you if pressure is bleeding off for some reason, an injector pulse of 2.4 (seconds) is very extreme, it should be more like 2.4millisecond pulse. I take it you are not in the US? Since you are mentioning Bar for a pressure spec.

This is the Ford fuel rail adapter (diagram 1) from my own pressure testing kit, and it does look like a tire pressure port, even the threads look the same, that's the Ford test port, it's very common, I don't think they have ever changed it. But instead of trying to use tire pressure sensors, (since those are designed for air pressure and not liquid fuel),

You could get one of these 80psi pressure transducers (diagram 2), I have adapted the pressure transducer with some fittings so it will go onto my fuel pressure testing hose, and although I use this setup with my oscilloscope to monitor pressure or do fuel injector balance testing, you could still use this setup without the scope. The transducer is a 3-wire sensor, so it has a 5volt power feed (reference) a Ground and a Signal wire. The signal is 0.5-to 4.5v roughly (basically 0-5v) like many other 3 wires automotive sensors on the vehicle. I used an 80psi transducer since that's about the highest pressure I'll be using this particular one for. So near 5 volts is close to 80psi (5.51Bar). Then you could run the wiring into the vehicle and have a meter with a voltage reading on it.

The pressure transducer does require a 5volt feed, but I could help you get all that figured out. The throttle position sensor uses a 5volt reference as well, so you would need to just run a signal wire and a ground wire into the vehicle so you could monitor the voltage on a little display inside. You would see the voltage drop off if you are losing fuel pressure.
A pressure transducer and a small voltage meter are very cheap, the tire pressure monitors will fail very quickly, and they are also battery powered. But we could get you set up with something like this if you would like, since you are switching between and using both systems.
If I divide 80psi by 5v, that's about 16psi per 1volt.
The fuel pressure spec is 45-60psi for your vehicle, when I looked up the conversion 3.3Bar is about 48psi.

Without messing with the MAF, just take a look at the live engine data with the scan tool, there will be a data PID for the MAF, for a 2 liter engine or around 2.0 liter you would have about 2-3 grams per second (g/s) reading from the MAF, another data PID to look at is the Long Term and Short Term Fuel Trims, they will read in a percentage (%), either positive or negative. So, for example if you see +10% for Long Term Fuel Trim, the PCM is adding 10% fuel to the air/fuel mixture to get it back to the 14.7 to 1 ratio, this is how the PCM compensates for any vacuum leaks, clogged injectors, etc. So, the vehicle will stay within emissions. Standards. It sounds really technical, but this is basic fuel strategy for the PCM.
Sorry for my long post.

Some sensor grounds are shared inside the PCM and some sensors use their own ground to the engine block, some need to be grounded internally to the PCM to reduce noise on the sensors signal, some sensors are analog sensors and therefore require that the signal goes through an analog to digital converter so they can be read by the PCM, and the grounding internally helps to keep a low noise, accurate clean signal. Some sensors use external grounds, it really depends on how the manufacturer has designed the system. The Intake Air Temp sensor in this case uses a share ground with a few other sensors because in its case the PCM is monitoring the 5volt reference it sends out to that sensor, if you were to unplug it and check the voltage level on pin 1 it would read 5volts, but plugged in it would read whatever the voltage level is according to the resistance of the sensor and that's how it measures the air temperature coming in. Pin 3 is a shared ground going to the engine as well as the PCM.
Are you finding grounds with high resistance readings?

Okay, when you say pins 2 (green/red) and 3(black/orange) you're putting your meter leads across pins 2 and 3 and getting 12v? Pin3 being the Ground...
And Pin 4 (brown/blue) sensor Ground and Pin 2 is 12volt supply. Sounds like you have damage inside the connector.
Try measuring Pin 2 and use Battery Negative as your Ground. Key On, if it reads battery voltage, so your 12.7v then you have a bad Ground on Pin 4. Since you can flex the connector and get the full 12.7volts to come back, the issue is isolated to the connector and shouldn't be a bad ground through the PCM. You can get a new pigtail (connector) for the MAF and just replace it. Thats what I would do, just go one wire at a time when cutting the wires and crimping a heat shrink connector. Here is a video on using Heat Shrink connectors and a picture of crimp pliers, notice the color markings on the pliers, those are for the size of heat shrink connector you are using, make sure you crimp the wire onto the connector tight, the video shows a little tug test to make sure it's a good connection, then you can use a lighter or whatever you have to heat the connector and it will seal around the wire, this keeps any moisture from getting inside and protects the connection.
You'll see how fast the cover shrinks around the wire, give it a minute to cool off and you should be good. You can do a search on YouTube for other videos that will go into more detail if needed,
The new connector for the MAF should come with a few inches of new wire already pinned into the connector (2nd diagram). Even if the wires are all the same color, just go one by one from the old connector. so, they don't get mixed up. But that's a good find. Flexing the connector like that revealed an issue.

https://www.youtube.com/watch?v=aij2ve4iq-A

Just go get a pigtail from AutoZone, don't order parts from AliExpress, that's worse than Amazon parts. And you can get a small box of heat shrink connectors there, a 10 pack is $8, or here's the entire kit for $33. Repair it the correct way the first time or you'll just end up with wiring that has corrosion inside the insulation, and you will have to replace even more wiring. Get a can of Mass Air Flow cleaner spray while you're there and clean the hot wire inside the MAF, I guarantee the wire has dirt and build up on. Follow this guide to clean it,
Once the MAF hot wire gets dirt on it the sensor under reports the air flow and it drastically affects the engine performance.

https://www.2carpros.com/articles/mass-air-flow-service