IMO, it’s not the full story to say the Republican party was a third party that year. The previous opposition to the Democrats had a rift and came apart. I think you are underselling what “the right conditions” are. This is more like a new party filling a void.
That year the Democrats themselves (regressives as this was well before Southern Strategy) split into two. Running both a candidate for “states’ rights” style slavery and another for “fuck you, slavery everywhere” style slavery.