What he said- no mop on goop is going to reliably find the leak, let alone last for a couple of years.
If there are more than 2 layers of shingles the odds of being able to find & fix the actual leaks goes way down. Stripping the tons of asphalt down to the roof deck (for inspection & potential repair) and starting over is the right thing to do. Spotting where it comes through the roof deck could be many feet away from where it's actually leaking.
In the mean time you can put something in the attic to keep it from soaking the insulation and ceiling gypsum it may mitigate the ongoing damage, and attic mold, which may not be too bad if the soaker storms are very infrequent.
If you're going for the mop-on approach, if you can spot where it's coming through the roof deck and slather on any vendor's fiber reinforced liquid wet/dry patch product from the interior leak point all the way up to the ridge in a 2 foot wide path you may be able to at least slow it down for a long period of time. Get a 3- 5 gallon bucket, not just a tiny tub- you'll be re-applying and doing a lot of trial & error before you get it all. Be prepared to throw away the clothes you're wearing when applying it. It only seems to come in one color- asphalt-black, and won't be pretty if you're doing 2' wide stripes up the roof, but you'll probably eventually be able to patch/re-patch and hang on for several years on a single 5 gallon bucket.
If it isn't obvious where it's coming through the roof deck you may have to lay down some sheets on top of the insulation and keep checking for wet spots after every rain. Don't assume that it didn't leak just because it didn't drip through into the living quarters. If it's coming through a nail hole or soaking through a punky spot in the roof deck it will probably be directly above, somewhere in that 2' wide path. But with 3-4 layers of shingles water can move laterally quite a bit on it's way down. If the interior side leak point is at a seam in 4x8' sheets of roof decking the actual leak may 5 feet more laterally from that point, but always above the point where it's coming into the attic.