Thanks for looking, darthviper and Zac. Reflection probes are in place, I even tried a few more around the object to see if they make any difference (they didn’t). The whole object has metallic properties, but strangely only parts of it go dark.
I tried lightmap resolutions of 64, 256, 512 and 1024 - didn’t make a difference, except that more was black with the 64 lightmap if I remember correctly. I will try a bake on grey basecolor tomorrow, great idea!
Here’s a quick wireframe: