Cute idea, but for fun I'd mix in the current year somehow. And birth year. Sort of chinese+western zodiak.
In my head, there are 4 5e core achetypes; warrior, trickster, mage and priest. There are 2 classes in each one, plus 2 impure "hybrids" adjacent, plus artificer.
Dividing the year into 13 pieces is fun (pseudo lunar!). A 4 year cycle for archtype, modulated by pseudo-lunar birth month? A number from 1 to 3 (second year cycle? So 4*3=12 year cycle), plus one from 0 to 1 (even-odd birth day digit?), to generate a number from 1 to 4 with less probability on the end (for hybrids).