Undeniably some cauls were made using filet lace (net) however this technique puts a knot at each intersection and this would cause problems adding the pearls, and if made with a plaited cord, the knots would be quite large.
It is possible one long braided cord could be made then stitched at each intersection however this method would require some pretty invisible stitching, and there would be an effect of one cord being higher then the other at intersections.
To achieve the plaited effect of the cord and intersections that are suitable for adding pearls to, plaiting the cord as the caul or partlet is constructed is the only real answer to the problem. I've made up a pattern for a small caul (possibly too small) and it requires about 106 bobbins, that many strands without bobbins would just be unmanageable and tension would also be difficult to maintain. As such I believe bobbin lace is the method which was used.
The other detail images in my last post are from the portrait of Eleanora wearing a red silk gown.
The partlet and caul Eleanora wear with her red gown is of gold picots with a silver stripe down the centre. Possibly cord could be made to achieve this effect using techniques I am not very familiar with but again bobbin lace solves the problem.
In yet another Bronzino portrait of Eleanora with her son Fancesco, Eleanora wears a partlet which again has a plaited look and is mounted on a fine sheer fabric. Perhaps it was embroidered to get this effect? As to the caul she wears in this portrait I have not been able to get a high enough quality image to see any details.
And in this portrait (after) Bronzino the plaited cording on the partlet again makes an appearance, you can just see the plaiting detail on the caul as well.
Well, I hope I have explained why I think bobbin lace and not fillet lace (net) was used for making Eleanoa's cauls.
What method do you think was used?