leaking vented tile

FFHillbilly

for about 6 months a little bit of rain has been getting into my cooker hood vent whenever it's really wet. it's on a pitched roof (17 degrees) and water appears at the lowest point of the 100mm spigot inside.
I have looked at the vented tile many times and I haven't seen anything obvious, thoughts were it could just be getting in the hole in the membrane and was a problem further up but after ruling out other things it looks like this might be the culprit.
where the cowl part is bonded to the tile I can see the paint has worn off the adhesive, and there are a few tiny holes. this isn't the exact type but it's similar:
I want to try sealing it again with something, but don't know what to use, any ideas?
would this do? https://www.ebay.co.uk/itm/202475206374?