When I got my coupe 2 years ago it did have a motif bar, but it wasn't fitted because the special rubberised mounting bolts were broken.
When I finished reassembling the car for the second time I bought new rubberised mounting bolts and refitted the bar. It fell off the same day because the replacements broke too. Fortunately it stayed inside the bonnet "mouth" so it wasn't lost.
My roadster didn't have a motif bar fitted at all when I got it; presumably it had suffered the same fate but had been lost.
I sent the coupe's bar off to be rechromed with all of the roadster trim, and bought a repro one, and very nice it looks too.
As the two are the same I decided to fit the new one to the coupe and put the old rechromed one on the roadster.
With the usual "how hard can this be?" I headed off into the shed.
Firstly I had to fit the motif itself into the circular hole at the front. This is held in a circular metal backing, which in turn is secured in place by a half elliptic spring that is screwed at either end to little pillars on the back of the bar. To be honest this seems overcomplicated; a dob of glue would have worked better.
Now the first issue that became apparent was that no screws were provided. There were 2 holes but they weren't threaded. On closer inspection they weren't even remotely parallel either, nor were they in any way centrally drilled into the little cast pillars the spring attaches to.
After a bit of thought I elected to use stainless self tapping screws to hold the spring in. Excellent idea up until one snapped off in the hole. Dremel and drill cleared out the hole, albiet bigger.
By now I'd used up about an hour. I decided to tap the holes for 8x32tpi cheese headed setscrews. Also an excellent idea in theory, but of course in practise it was largely impossible because there was no room for the tap...
Eventually I managed to tap the redrilled hole using a small spanner to turn the tap; a rather slow process.
The other hole I left as it was and railroaded a 3mm hex headed high tensile screw into it.
Finally, the Jaguar head motif was installed.
Now all I had to do was install the bar into the bonnet. Firstly the old rubber head bolts had to come out. These are classic Jaguar; you can't see them and you can barely get to them. Eventually I managed to remove one with a 1/4" drive 7/16 socket on a screwdriver handle, but the other one was of course too tight. When installing the fuel pump I bought a brilliantly designed 1/4" drive ratchet handle which turns when the handle is rotated axially. I just managed to get the socket on the head and despite working about one click at a time I succeeded in removing the bolt.
Now to be honest I have no idea why the motif bar has to be mounted on its own shock absorbers, so I decided to just bolt it back in using a couple of 1 1/2" long 1/4" bolts, which seems to have done the trick.
Surely a solid bolt can't possibly be any worse than those stupid rubber things...
Total time; about 3 hours.

 It's fascinating to reflect on the level of overengineering that has gone into this simple part of the car. In a way it's quite un-Jaguar, who frequently looked for the cheapest solution. I'd love to meet the designer and ask why..