You’ve received some great thoughts, especially by Paul Thomas where he talks about checking your client’s ability to do steady-state cardio without dizziness.
You’ve mentioned that your client is healthy, but have not mention how fit he or she is in general. Your client might need more warm-up before engaging in HIIT, and a more gradual cool-down. Also, HIIT is a very individual thing; if you’re committed to giving this client a HIIT workout, you have a life-enhancing reason to do so, and you’ve determined that your client can do steady-state cardio without the same symptoms, adjust the HIIT exercise so that it’s a smaller increase above what their “normal” cardio is. So, for example, if they’re comfortable with an RPE of 5, instead of going from 5 to 9, to 5, to 9, try an activity that goes from 5 to 6, to 5, to 6, to 5, to 6. See how the client tolerates that. Then 5 to 7. And so on.
Also consider whether the activities themselves might be the culprit. Are you doing burpees or other things that drop and raise the head suddenly?