The Mustang stock oil pressure sender is a simple on/off switch that works at 6 PSI (yes that is correct!). So assuming the sender is working as designed, if the oil pressure dash warning light comes on it means oil pressure is below 6 PSI.
First, the oil pressure sender can and does go bad. They are cheap and easy to change. However in this case it seems unlikely to me that this is s a false low oil pressure because the lifters start making noise.
If this were my car I would get an oil filter cutter and cut the oil filter open looking for debris.
Not a bad idea to actually measure the oil pressure with a real external gauge.
Given the high mileage on your motor I'm afraid the final answer will come down to excessive main bearing wear. But it's always best to check the "basics" before moving onto the big $$ items.