I created new trait with definition like in attached picture. When I am selecting audiance for page variation and this is only trait I select and I leave checkbox un-checked then audiance info is not saved in Magnolia repository.
If I check the box and save it and then remove check by editing then audiance info is in repository also if I combine it with other traits I get expected results.

Also attached configuration xml and module code. Module code needs some tweaking to run in your environment, but I hope this might help with recreating the issue.