Just purchased 1994 Mercurty Sable - 134K mileage,3.8 motor. Ran great. Then quit. Acts like srtarved for fuel. Would restart - but not keep running. Thinking fuel filter or weak fuel pump. Ignition switch appears loose, but car starts anyway.
Could be a fuel problem. A new filter certainly can’t hurt anything.
A loose ignition switch could also be the culprit.
I think you’re on the right trail. Filter and pump would be my first guesses. Mechanic can put a fuel pressure gauge on it to check.
My brother had a van coming to see me when He stopped at the toll booth and started back up it just quit on him. Ran fine till then. Turned out to be the fuel filter. I’d change it first. Did the former owner tell you when he had it last serviced with all the filters changed? If he didn’t I’s seriously would think about doing so while you’re at it.