Stop in for a cup of coffee

Flex seal the whole thing. Gallon cans and a roller and it will never leak again!
There's a acrylic Rhom and Hass developed that a couple companies have been making into a effective coating product for rusted tin and similar situations. Acrymax is the best known. I've used it, and it works well when done correctly on a metal substrate. Like any coating it needs to go on a clean surface. But even on a rusty tin roof with asphalt and other cr*p it works well as long as the rust has been scrubbed and primed. Rustoleum Rusty Metal Primer works well for this. If the surface is weak or has holes, its worth the trouble to embed in an polyester fabric mesh. Then top coat with a slightly denser forumula they sell.

I did that on a nighbors house which still had its original tin roof (100 plus years!) and also a sloped section on my back bay after pealing off many layers of failed built-up rolled roofing products.