Vexillology = vexillum + logia
Vexillology is not a historic subject of study, it was not in the Trivium of grammar, rhetoric and logic, and it was not the Quadrivium of arithmetic, geometry, music and astronomy.
Vexillology as a distinct focus (and a focus is a looking towards, into, amongst something, not looking out and out and out)is pretty recent in history, though contains some finely focused minds, and here is the reference – https://fiav.org/the-origins-of-organized-vexillology/
Because similar interests gravitate towards each other (gravity as the underlying principle of the whole of existence on Earth and without it where would we be?), within a few decades the focused interests had developed – https://fiav.org/wp-content/uploads/2021/06/ICV20-28-Schmoger-The-Roman-vexillum.pdf
In layman’s terms (the non-expert), the vexillum was the portable square red cloth hanging from a crossbar, so facing head on, therefore designed to be visible. Velum = sail in Latin. It was the only cloth flag of the Roman Empire and when there is only one, it is possible to define the meaning, or the message, or the point of it, or the function. The letters SPQR – Senatus Populusque Romanus – define a totality of geography, a place, governance, and citizens, but why would someone bother to go to the effort of making such an object? It was for military function, to define Roman jurisdiction and territory.
The vexilloid, also a relatively recent term and from Whitney Smith, likewise did not create something new but the slightly different word defines the difference between the cloth flag and the staff with carved emblem. A vexilloid equally defines from within, and looking over the whole Earth (which a human cannot do, except through modern digital tech which is all going down at the next big solar flare) that symbol of a wooden staff with carved emblem and local relevance such as feathers is still a fundamental part of indigenous societies,
The combination of language and physical objects arising from the ve – velum, the various vex’s, the focused knowledge within vexillology and the now Vexed question of Vexillology, are all from within the trajectory of the Roman Empire, to be still lodged within the ‘UK’, the further possible landmass (taking the Channel as not too hard to cross) of western Europe. In Europe we do not have vexilloids now, apart from ceremonial function of state and religion, and historical re-enactment societies, but we do have a lot of vexillums, as being a cloth on a pole.