While we were up there on the upstairs porch doing that, I pointed out how badly filled with leaves and dirt the gutters are. Lisa climbed over the railing onto the roof and dug out the gutter with a stick. As our roof is much flatter than the house in Mehama, she didn't consider this particularly dangerous.
After dealing with that, we went back down to ground level and Lisa inspected the downspout. It turns out that over the years, sand had blown in around it and blocked it, and plants had grown up inside the spout itself. Lisa got a ladder and unscrewed the downspout. I used clippers and a shovel to dig it out and after removing it from the gutter knocked out the accumulated dirt and roots to clear the spout. Then I dug out around where it should go to give it enough room to drain and Lisa put some rocks in the hole so draining water lands on the rocks.
We don't get much rain here in Fernley (around five inches per year), so this hasn't caused too much trouble, but when it does rain here, it sometimes rains quite intensely, so we want the drains to work.