When originally constructed, the Tardis was done on the cheap. I tried doing the roof with some scrap aluminum siding that Grandpa has directed me towards at the dump.
This worked fine in all weather except for rain, snow, sleet, etc. As long as it was dry outside, we were dry inside.
Donna didn't really approve of that situation, and I recently learned that my own mother also was put out by having icy cold water dripping on her while she was enjoying some solitude on the throne.
One of my first attempts at a solution was to purchase some of that "tar in a can" type of product, and heavily spray down the seams in the siding. This didn't do anything to help the situation.
Using up a few tubes of latex caulking also didn't seem to find the location of the leaks.
At last the solution presented itself in a serendipitous manner - the steel roofing for the sauna came with two brown "cover sheets".
I aired myself out on a particularly warm day, and then set off to redo the roof.
It took a fair bit of coaxing to remove the lantern from the middle of the original roof, but after that, I was able to lay down the sheets, install them, and replace the lantern with a minimum of fuss.
I wasn't able to get the lantern to sit perfectly flat, so I just goobered on a tonne more of caulking as an adhesive, and things were good to go!
So far, everyone has been quite pleased with the solution.