Concrete gutters - external leak advice

Ok so I know this is going to me met with ‘cut them off’ responses but that’s not going to happen.

I’m mid terrace, have concrete gutters and hanging wall tiles over the brickwork

Where my concrete gutter meets next doors, it’s leaking at the join between the two linings, and dripping through the join between the two sections of concrete. This then runs down the hanging wall tiles so isn’t causing any damp (I don’t want to jinx it but touch wood it’s not caused us any problems yet) but I still want to fix it because it looks naff

Will patching and sealing the join do the trick or is this likely to need the concrete join repointing as well?

This is going be a diy job between me and the neighbouring property

Thanks for any advice that isn’t “chop them off”