Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Panama to Eugene as you normally would.
In terms of precipitation, rainfall in Eugene ranges from 0.5 - 7.8 inches per month. December is typically the wettest month, when rainfall can reach 7.8 in. July is typically the driest time to visit Eugene when rainfall is around 0.5 in.
If weather is an important factor for your trip to Eugene, use this chart to help with planning. For those seeking warmer temperatures, July is the ideal time of year to visit, when temperatures reach an average of 66.2 F. Travelers looking to avoid the cold should look outside of December, when temperatures are typically at their lowest (around 39.2 F).