Rear view mirror vibration

Tighten the windshield dow-rod slightly. Not too much, the windshield could crack.

Does it vibrate from the engine revs? Put the car in neutral at speed ahs let engine idle. Does vibration go away? If so, clean idle jets and synch carbs.

I would change out the rubber for a more dense material - clear piece of plastic hose, the rubber may be part of the issue an as Danny said snug up the center post nut a bit.

I put mine higher than yours, so that it is closer to the frame of the windshield and it reduced vibrations a lot. Still happens. But now I can tell it’s a crown Vic not a civic. 

"It's not like I can't make out whether there's a car behind me or not, but I think it's reasonable to believe it could/should be more steady.  "

Nope, they all vibrate.  It's more like a suggestion of what might be back there.  Mine is only semi-useful, most of the time.

And the rubber you applied probably made it worse (or at least,  as you found out, it didn't get any better) because it allows both the mirror rod and the clamp against the windshield strut to vibrate, too.  

The best thing would be to apply the metal clamp directly against the mirror rod and windshield strut, no rubber and crank it up tight.  If that doesn't appeal to you, then a piece of semi-rigid vinyl tubing on both the mirror rod and strut should be better than the rubber piece.

I also don't think that making the windshield center strut tighter will do much and it might make the windshield crack from stress (and none of us want to hear about that).

My mirror doesn't vibrate at all. My center rod is tight. My windshield hasn't cracked. My mirror is as high as it can be but still allowing vision through the top's window.

I have a solid rear(front for Speedsters) engine mount, and a solid metal trans strap. Again, no mirror vibration. I'll repeat what I said in my post above, get the mirror to vibrate, then push the clutch in and let it idle. If it's still vibrating 

I think I have a piece of tape wrapped around the tension rod, but rubber hose is a bad idea, it will only induce vibration.

And despite all the horrors associated with windshield removal, I've never broken one. I've had the windshield off about 5 times, same frame and glass, two different cars. 

Don't crank the tension rod down to kingdom-come, but just tighten it so it has enough tension not to vibrate.

Hmm, there may be something here wrt the carbs.  As I've mentioned in some other posts, my carbs might need adjustment at least for the lean/rich odor.  I did try rotating the screw to either end and finding where the engine would start convulsing, I'm pretty sure I left the screws between those points and so there isn't shaking (but will confirm in a few days).  But I have to admit that there was a lot of window between those two end points of the screws on either carb, so some finer tuning probably can be had.  Whether that has bearing on this vibration I don't know.

Either way, I'll back track on the rubber "dampener" and observe the difference just out of curiosity.  Perhaps I'll have someone capture a quick video clip so that you all can judge it, if vid captures it accurately.  

I'll play with moving the clamp position up and down, but there's probably only so much of a range available based on the driver's head position.

The tension rod is pretty snug if I remember correctly, in fact I had to tighten it recently because I had entirely removed the rod to refinish it.  Side note, it had a bunch of teeth marks from the clamp, a bench grinder with the sponge-like rotational bit did a beautiful job of buffing those all away.  The whole rod looked brilliant, but I wasn't sure what the material was therefore whether it would oxidize, so I spray painted it chrome.  Yes I know, that's the duct-tape approach.  Figured I could always remove the paint if it looked bad, but it looks surprisingly good.  You can tell the diff wrt real chrome finish in the zoomed photo above, but you wouldn't notice it from normal distances.  In fact I was thinking to write up a post about my findings of how different chrome/metallic spray paints performed, and compared to just using a clear coat spray... Anyway I'm drifting in my own thread here.