You might find problems removing the nail with the slate ripper.
How to stop a slate roof leaking.
Installing a bonding gutter this video shows a roof repair and the fitting of a bonding gutter between a slate and a tiled roof but it will also fit two slate roofs together as well.
Beware of using asphalt roof mastic on copper flashings it fixes the leak in the short run but corrodes the copper in the long run.
Details are at slate roof leaks temporary repair.
Begin soaking low on the roof just above where the leak is visible inside the house.
Once you ve found the problem slate you need to remove it.
Insulate the smallest space possible.
How to repair a leaky roof from inside the house.
You could make a temporary patch using stick down materials or on some roofs i ve seen roof mastic used in that application.
Shine a flashlight along the underside of the roof and look for a hole in the roof as well as areas that are wet or have been.
Apply more tar over blocking material especially on the edges.
For example soak the downhill side of a chimney first then each side then the top on both sides.
You can use either a dry bonding gutter or the standard bonding gutter.
With good wire cutters you might also be able to cut off the head of the nail which will help.
Insulate the roof if you are going to finish the attic if not insulate the ceiling.
Run water over the low side of the penetration for several minutes while the helper watches for any water droplets.
Have your helper stay inside the house waiting for the drip to appear.
To do this use the slate ripper to rip off the nail that hooks the slate onto the slate roof.
Start low soaking the area just above where the leak appears in the house.
Apply tar to the area and press blocking material into the layer of tar to cover the leak.
Isolate areas when you run the hose.
Go nuts with the vapor.