I have tried adding linetype to the aes but it does not change anything....This shouldn't be this hard but I'm at a loss.

Sometimes the overabundance of specialized functions combined with the aes-legend linkage can make custom legends more difficult than in base R graphics. But this seems like a pretty typical use case and you're right that putting linetype in aes() is the way to solve this. Your precip dataset isn't the R precip data, so here's a simple example that seems to do what you want

ggplot(data = mtcars, aes(x = wt, y = mpg)) +
  geom_line(aes(linetype = factor(am, levels = c(0,1), labels = c("Manual", "Automatic")))) +
  scale_linetype_manual(values = c("twodash", "solid"), name = "Transmission") +
  geom_point(size = 2) +
  labs(x= "Weight (Tons)", y= "MPG") +
  theme_classic()