Sadly I am not sure that is a solution.
It appears that without converting to "Game Base" the character is not given a suitable skeleton for Unity to import with a Humanoid rig. I will keep testing.

Thank you Bassline303! You are a legend. I will test that out.

There are 2 other ways...

Hi Everyone,
I just posted a request to increase the Max Texture Size when converting to Game Base. I have been exporting characters to Unity and I am seeing a lot of detail loss due to the 2K limit. I am hoping that it will be quite easy to add an option to allow up to 8K textures?
If anyone else would like to up-vote this request then here's a link to the issue:
https://www.reallusion.com/FeedBackTracker/Issue/Increase-Max-Texture-Size-when-converting-to-Game-Base
Thanks,
Rich