there are books ( old ones) that have many recipes for patination. google will get you enough to keep you busy for a day or two. one i used to use was antimony pentachloride. it would deliver a nice green in very little time. patination, like most engraving related issues, doesn't just happen. even with a recipe, one must expect a learning curve.
Brian maybe we have the Corioles forces affect at work here which explains the various behaviors of chemical patina solutions in the northern and southern hemispheres!
JAX Brown or JAX Brown Black both work very well. As mentioned, you will probably need to highlight the piece with 0000 steel wool and/or Sunshine cloths.
I have both of them. Get the second one from richard hughes it has all that is in the first plus many hundred more recipes. For variegated browns on copper/copper plate it lists 63!! different patina formulas ,not counting all the other colors or other metals... should be something in there that gives you the desired color.
The second one may be less usefull to you because its in German but since its cited many times in the book by Hiorns I included it anyway.
Some of the formulas you still find unchanged in modern books - others not because they use rather toxic chemicals we dont want to deal with nowadays.
To elaborate a bit on my previous posting: The Runfola Book has lots more flashy photos and covers the actual process of how to patinate a bit more in detail, if you have never patinated anything this might be a good choice for beginners. Actual patination formulas for all the presented metals just cover about 2 pages though with some of these commercial solutions without the recipe given.
The hughes Book is older and does not have so much photographic detail on the actual process, still all the different patination techniques like immersion, fuming chambers, cold and hot application, sawdust technique etc etc. are covered. There are some photographic color plates to show results of different formulas but there is NOT a color plate example for every different formula. That would be hard to do since patination formulas cover pages 67-332 with about 5 recipes per page... Short instructions on how to use/apply the recipe are given for each, sometimes with additional comments on particular specifics relating to the chemicals or application technique and varying the result.
Overall the information density is much higher here than in the Runfola book but its mostly pure information. If you are big on visual instruction the runfola book may be better for you - but it has MUCH less to offer in the way of actual recipes.