I have thought about this rattle more than once, but this thread has me revisiting my efforts. For the majority of the 7 years of restoration, I never noticed the rattle because as Don stated, it happens "only at idle". When I first had the car running with the hood on, it had what I assumed to be an original rubber retainer for the stay rod. The rubber was old, covered with multiple coats of paint, brittle, very hard, and began to tear shortly after it was installed. I had other rubbers equally as original, but they either started to tear after installation, or were unable to hold the rod, so a new one was purchased. Also, the rivet and bracket at the other end were rusted and needed help to move before I painted. By the time they were assembled, the rivet was again tight because of the paint that managed to seep around the edges. I don't know when I first noticed the rattle, but the rattle was erratic, even after the idle was stable. With the ability to bump the idle a little with the choke pull, the rattle will still come and go at different idle speeds.
If I understand resonance correctly, it is rather finicky. Either end of the rod could effect it, as well as anything touching the center, as well as the stiffness of the rod and probably even the temperature of the rod. My idle can be between 800 to 1200 but I haven't found a sweet spot where the rattle will not (ever) happen. I think Johns 600rpm idle is amazing low and doubt mine can reliably idle that low. I have a TR4 cam in mine, but under 900rpm or so, it searches a little, almost lope-like, probably the result of the distributor springs over-reacting. -anyway, the rattle doesn't always happen when I stop a red light. It does seem to always happen when a pedestrian is showing interest in my TR3 while it is idling.
My rattle may have become more noticeable for several reasons. 1)it is capable of idling 2)the idle is relatively smooth 3)other functional issues are comparatively small 4)the paint has worn away from around the rivet on the front 5)the rubber stay rod holder is soft rubber. -Giving this much thought to a single rattle in a toy car over 50 years old, makes me realize just how lucky I am to have it.
I may add a rubber o-ring on a string instead of the "original" holder for the stay rod and hope that resolves the noise completely -or I might just try to remember how lucky I am to have it rattling.