I think it depends on what the down stream process is, the etchant used, and the strength, i.e., if it is buffered or not.
You could take a look at ASM literature to see what information they have. Their books aren't inexpensive, but you get what you pay for.
Best regards - Al
Milton
Are you chemical milling, architectural staining, or just etching for Metallagraphic effect?
In addition to Als response, temperature will have a direct effect, hot=faster, cold=slower, and the echant can become depleted from use and exposure to air.
As You are only etching the wetted surfaces, I don't see material thickness being the issue, but if You are removing oxides/anodising, coating thickness will be a factor.
What are the other processes ?