Interesting, and even strange to my old mind.
I think your experience is about controlling/evoking body functions that stimulate the heart system. What are you doing with your breathing during these "tests"?
Anything we do that changes our oxygen intake or need changes the HR.
I recommend against forcing your breathing (holding or power breathing) to see what it does to your heart.
It's not common; or at least I don't think it is. Since you got chest pain and a headache, you should probably contact a doctor, as this could be serious.
Well you can, at least I presume that you can control your parasympathetic nervous systems to some degree, indirectly by such things like how you breathe, you sit, certain postures and so on.
Or when you elicit that feeling of being light, that could sensation since it would stimulating I imagine may very well be what triggers the rise in your pulse rate.