I recently finished a deck and with it I built this laundry housing. I used tongue-and-groove redwood siding. I love the look, but as I suspected, it's not waterproof.

So, I'm thinking I should add shingles. I've never done this, so this should be a good place to start .

The redwood siding is only .5" thick and as you can see there isn't any backing for nails to go into, so any nail longer than .5" is going to poke through.

Can I glue shingles on using some sort of construction adhesive? Again, this isn't a house, so the stakes are not high, and it certainly doesn't need to meet any code requirements. I just want rain to run off rather than seep through.

Any suggestions would be welcome.