from some of my own 'watertight' experiments, I found silicone will 'stick' to pvc but not exactly make it watertight. If you scuff the plastic, it'll hold better (supposedly; am still experimenting). That is, it DOES adhere but you can peel it off pretty easily after it sets up. There doesn't seem to be a lot of great options for this, though there are some pvc-friendly epoxies (I haven't tried those as I need to be able to get the seal off and the epoxies look to be permanent). That said, imo, it should work but just pay attention if you ever have a leak, check at the silicone seal first.
You may be able to just put silicone in the bowed openings, esp the top. Did you silicone the pvc gutter to the wood? Doesn't look like it. Also, the wood, esp if it gets wet, is going to swell. And then you'll have contraction when it heats and/or dries out. Not sure how much of either you'll get, but it's something else to watch for. Were it mine, I think I'd have put the liner all the way through to keep the wood away from any splash but rain is going to get at it anyway, so just realize you'll get some expansion/contraction just because it's wood.
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