Try wiggling the connection, i believe there is an O'ing inside.
You mentioned tapping the brake pedal got a reaction.
That leads me to ask you about this.

 

Ok sorry for the delay. I have wiggled the vacuum line going to the brake booster and no change in rpms. Recently I ordered a used MAF from a used jag that had 85k miles. I installed it and there was no change to the performance it still had the rough idle and no CEL. I then decided to order a denso MAF from partsgeek.com which I have got many parts off of and had no issues with quality. I got it in and installed it. The MAF looked the same as oem one but just had "denso" on the top of it so it didn't look like the oem one where it says made in Spain. I drove to work and back still having a rough idle but I noticed an increase in power. It felt like it used to feel not sluggish. This got me thinking. I arrived back home for the day and BAM the engine shut off and I got a p0102 code. I assumed the MAF was faulty. I took it out and put the old one back in and the code reset right away and has not come back on. What is going on here!!??

 

If I have a vacuum leak I don't know if I would ever find it. I have gone over every hose and gasket and still nothing to suspect.

 

Many possible locations. You may need to "smoke" test the system.

 

**UPDATE**
I think I have finally found the cause of my rough idle. Yesterday I was messing around with the EGR valve which is not easy to take off and cleaned the whole part again but this time I sprayed berrymans b12 carb cleaner into the valley hose and I sprayed a lot not thinking anything of it I just figured why not what's it going to hurt put everything back together, started the car VOILA! my jag has never ran so smooth! I'm positive now that it was been carbon build up this whole time. Makes sense with no CEL coming on.

 

I have a 2002 Vanden Plas 4.0 with exactly the same problem. Actually I purchased it from a senior lady whose garage billed her a few thousand replacing everything as you listed but it continued. I bought it and brought it home and searched for vacuum leak and then did a compression test. While cylinders 1 to 7 are between 185 to 200 number 8 turned up ZERO. Not even moving the needle. They replaced plugs and coils and O2 sensors on and on. As there is no water in the oil or hydrocarbons in the coolant I an ruling out head gasket. It doesn't overheat. It just runs exactly as you post. I blasted air into the cylinder and it came out the throttle body which indicates an intake valve is open. Whether it's a broken stem or a brioken spring that means off comes the head. I suggest you do a compression test which is very simple on the Jag engine.

 

Sorry I read your post before the last update and didn't realize you discovered the solution already when I added mine. Glad you don't have my problem

 

Well, glad you found your "vacuum leak"! As you suggest it was probably carbon holding the EGR open some.