FWIW, consciousness has no properties and so cannot be studied scientifically.
However, consciousness can be explored experientially, i.e. two conscious beings can merge and experience self as one being. (See Charles Tart's experiment with mutual hypnosis.)
Can you give at least a rough sketch or gist of the argument you are referring to?
1. Purely immaterial things exist. Think of mathematics or the laws of logic or physics - these things exist as ideas or concepts, not arrangements of matter.
2. Some abstract concepts cannot be embodied in matter at all. For example, you can make a shoe, you can draw a shoe, but you can’t draw shoe-ness. You can understand and reason about what makes something a shoe in the abstract, but you can only make or draw an individual shoe.
3) the mind contains these purely immaterial things when we think about and reason about them.
4) If we can use the abstract concepts, but the abstract concepts can’t be embodied in matter, then the mind must be at least partly immaterial in order for the concepts to be in our mind.
I hope that helps a but please don’t rely on my exposition of the case - a real philosopher would do it justice.