In my opinion, you need the help of code.
Here is an article "Microsoft Office Reference Guide", although it is still a little far from what you need, but it points out we can use Control and VBA code to show the specified layer.
(Important! Follow the steps in this section carefully. Serious problems might occur if you modify the registry incorrectly. Before you modify it, back up the registry for restoration in case problems occur. )
As "office-visio-itpro" focuses more on general issue of Visio Client, the issues of VBA code needs to add another tag.
Thanks for your understandings.
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