Whoa, that's a difficult one.
First off. Domesplit, it's much better to get in touch with me using the PM system here on FF. I hardly ever check my yahoo email, and if I don't know who is sending me something on there I generally delete it with the 100 spams I get daily because I've used this email for like 10 years now.
The cats, well that's Fritz the Cat, and the girl is actually a dog, but you'd have to see the movie to understand that.
Well, a vibration can be due to a bad motor mount. You should be able to tell by the test I wrote about. Sometimes it makes a sound, but not every time. It depends on which mount is bad as to whether or not you hear a sound.
Vibration can be caused by other things. For example, I believe my van has developed a coolant leak into the combustion chamber of at least one cylinder. I'm hoping it's only the intake manifold. What happens is that the van is difficult to start, and runs with a horrible miss for a few minutes after starting. Once it warms up, the condition disappears. I found excess steam in the exhaust, but not horribly just yet. It's just a theory based on my experience with this particular engine, and I don't think that's your problem.
First off, if it was a motor mount, then the vibration would reappear at the specific engine rpm where you can feel it. That rpm is most likely to be on the low side, so you'd feel it at idle, but not while driving.
From what you wrote, it appears you have a bad transaxle mount, or rear motor mount. I'd inspect it visually for cracks or tears, and verify that is the problem using the motor mount test you quoted.
I'm sorry I can't offer more advice, but I'm better on extreme failures than on vibrations, clicking sounds, or other "sometimes" noises. There are times when these minor annoyance problems cost more money than extreme failures because you just keep throwing parts at the car to fix it- and nothing works. I have problems like this with my Focus, but I generally wait until the problem is severe enough for me to verify exactly what it is.
A hub, for example, will feel like a lot of things before you can verify it's actually the hub that's the problem. You might hear humming sounds like loud pavement while driving, notice a vibration when turning in the direction of the bad hub etc. Yet, when you jack that tire, and rotate the wheel with the bad hub- no sounds occur that identify the hub is bad. After changing the tires, wheel, rebalancing, alignment, and months of unanswered questions- the hub finally starts roaring, and when you rotate the wheel you can hear the bearings grumbling.
I'm sorry I can't give you more information than that, but that's how it is with some parts. As far as your tie rod, remove the wheel on that side, grasp the tie rod with your hand and see how it moves. It should move side to side- but not very easily. If the tie rod is floppy, just falling around without any force, then it's bad. You might even be able to hear a mid tone clank or tap just as the wheel starts to turn if you're standing beside the wheel. Generally, if you have a bad tie rod, you'll think it's an alignment problem, or out of balance wheel. You will also notice tire wear on the inside and outside of the tire.
