It actually makes sense that the carbon atoms would recombine to form every form of carbon in the high temperature of the flame before pairing off with an oxygen atom or two and flying off as CO or CO2.
This is not something I would have expected, but it makes sense. All possible reactions between reactants occur, but the kinetic or thermodynamic products are the significant ones we look for and isolate.
If you're at a university that can get past the paywall you can read it for free otherwise they want 32 euros for it.
The experimental setup seemed susceptible to aliasing (which is to say detecting one type of carbon when another was present) and the inability to extract the material measured makes cross checking the sensor difficult.