My front eavestrough leaks, onto my front step. It gets very slippery out there. When it started happening a few years ago, my neighbour politely suggested that a drop of caulking would solve the problem, and I agreed that it might. In the meantime, the concrete step tile below the eaves is sinking lower than the other tiles. I do have a ladder. I don't have a caulking gun. It's probably worth looking into, while the weather remains mild.
Update, December 4:
Cost of caulking combo tube/gun: $9. Time to apply it to the seam: 3 minutes.
