Spring and fall afternoons are your best bet.
Yes. For rainbows from a high tower, you want the sun low enough to create the arc, and you need rain showers passing by — which is most common in spring and fall.
The science is simple: rainbows form when the sun is behind you and rain is in front. From a tower, you have a wide view, so you need the sun at a low angle (generally under 42 degrees above the horizon). That happens in the late afternoon, and especially during transitional seasons when the air is unstable enough for scattered showers.
Summer afternoons can work too, but the sun is often too high, making rainbows lower or invisible. Winter has fewer rain showers. Spring and fall give you the sweet spot: decent chance of rain, sun low enough, and longer golden hours.
If you’re planning a trip, aim for a day with a mix of sun and showers, and be on the tower between 3 PM and sunset. You won’t see one every time, but your odds are best then.
