Still need that idle RPM...

 

It could be plenty of things. Without more information it's hard to narrow it down.

 

My edge says the idle rpm is bouncing right around 600 in park

In gear it it 530 at stop

I will look into it tonight. Was serviced last week. Vibration still exists

 

Speaking out loud here, but isn't a bit of a tremor kind of par for the course with these trucks? Especially with the 5.4 3V?

Mine has a very similar 'vibration', as OP describes. If I'm sitting at a stop light, I can feel my truck vibrating a decent bit. I'd akin it more to a 'rumble' than anything else. I can't say I feel it through the brake pedal or floor boards, but I can definitely feel it in my seats. Also like OP mentioned, this only happens while the truck is in park. If I shift into Neutral or am driving the truck, zero issues.

Here's a link to a video of a Taco Bell bag sitting on my passenger seat showing the degree of the 'rumble' - https://*******/e/ydrO Edit: That isn't air blowing the bag, just the vibration through the seats.

When I first got my truck, I asked about this very matter on the forums. No clear answers, but as people have mentioned, this is a COMPLETE wildcard. I took it to the dealership and explicitly told them to look at the engine mounts and take a seat in it and feel it and they said all of this is completely normal.

Since I've had the truck, I've cleaned the Throttle Body, cleaned the MAF Sensor, and replaced the Spark Plugs. I checked coil boots and they were in great shape. Transmission Fluid is nice and pink and there's no noticeable issues with shifting or driving. The 'rumble' still exists though.

It appears to me that this is just normal operating for these trucks. If anything, this post might ease your mind OP once a couple of people see my video and chime in.

 

Had the same Problem with my 2005 F-150 King Ranch. Changed spark plugs at 100k. The rough idle was nearly gone. 8000 miles later misfiring started and it run rough also at 2000rpm.
Tester said misfiring cyl 7. First thought the injectors, because the spark plugs are just new. But a look at the plug turned out, that the tip was broken.
Changed all spark plugs and the rough idle was gone for the first time.
After one day the rough idle was back.
Now changed the VCT solenoids and the motor is running like new. (old VCTs didn't look bad though)
Only in park I have a little rough idle. in drive or neutral it's fine now!
I also noticed better MPG now.

Could the defective VCT have caused the spark plug to die? (Got too hot or so?)
Why do I have the rough idle in park?