Can an Eevee evolve into Umbreon/Espeon "randomly"?

I am aware that there is a "naming trick" which you can use to evolve an Eevee into an Umbreon or Espeon.

I am also aware that you can walk with an Eevee for 10 km as your buddy, then if you evolve that Eevee at night/day, you will get an Umbreon/Espeon.

My question is: Is it possible for Eevee to randomly evolve into Umbreon or Espeon? So far, my random evolutions of Eevee have resulted in only Vaporeon, Flareon and Jolteon.

No, an Eevee will only evolve into an Umbreon or Espeon if it has been walked as a buddy for at least 10km and is your buddy at the time you evolve it.

If this criteria has been met, Espeon/Umbreon will be the Pokémon your Eevee evolves into. The determining factor for which of the two you will receive is time of day— a daytime evolution will net you an Espeon, while a nighttime evolution will result in an Umbreon.