It could sound like two male engaging in territorial showoff, – ‘agressive’ signaling to each other. I think often they then excatly does not stand head down, but stay side to side.
You may have a look at our – not at all finished page of P. phoenicurus – https://www.parosphromenus-project.org/en/p-phoenicurus.html here, – (you have to count your way down in the photoes) but photoes 8-10 and photo 18+19+21 I believe to be two males showing off to each other.
Have a look and see if you think it is this kind of behaviour your fish are showing.