make light

It's very unnatural.

But, would it be considered incorrect? Or would it fail to convey the meaning it's supposed to?

That depends on the context in which you say it.
Can you supply one for us to comment on?

I can't supply any one single sentence to explain the context, as it's part of a rather lengthy conversation. But, I can say that the speaker has been talking about a serious thing to the listener, but the listener has been joking about it for a long time. Will that suffice?

I wouldn't call it incorrect. But it is unnatural, as I said.

In addition, the meaning is not precise.
eg Am I making light of the situation?
eg Am I making light of the other person's concern about the situation?

Oh, okay. Thanks!