95 Mustang GT sputter and hard start at times

I’ve recently acquired a 1995 Mustang GT 5.0 from my aunt who no longer has a need for it after purchasing a new vehicle. I got the car after it was sitting in her garage for about a year and a half, and got a tune-up after getting it started. The fuel pump had gone bad as well as the fuel filter, so those were replaced. Here’s the problem. A lot of the time when accelerating moderately, the engine sputters and the whole car shakes for a few seconds, or if I accelerate harder. That is the minor problem. The REAL problem is that every now and then, the car will not start. Most of the time it turns over just fine and starts with a healthy sound. Other times, the starter just turns and turns but will not turn over the engine. After letting it sit for about 5-20 minutes, it will finally turn over and start. Sometimes when taking slow turns (5 mph) the entire car will shut off, and then will not start like I stated above. My mechanic I usually take the car to cannot find anything wrong with the car, and it is not throwing any check engine lights. Any ideas?

It would be helpful if we knew what went into the “tune up” - that term doesn’t give specific info. Is the check engine light on?

It would help you to find out if your problem is most likely fuel or spark. Stop by an auto parts store and get a spark tester and a can of starter fluid. The next time it won’t start, hook up the spark tester & check for spark. If you have spark, and can get the engine to run (even a little bit) with starter fluid sprayed into the intake then the problem is fuel.

That said, here are a couple of ideas. Fuel - Considering that it sat for so long you may have gunked up fuel injectors (varnish clogging the ends). Your options there are to pull the fuel rail, clean & check fuel injectors. There are companies that will recondition them. Or ask your mechanic (but maybe you need a new one?) for a fuel injector cleaning service. Or run some high quality cleaner through the system - Seafoam or Techron are two good options. I’d be tempted to start simplest - additive first, professional service second, then pull the rail.

Spark - I’ll assume that the “tune up” included spark plugs and wires. The spark plugs should be checked for proper gap and application - sometimes the wrong plugs do get put in. Also, if they’re not OEM (probably Motorcraft in this case) then you might try to go to OEM. The wires should also be checked for resistance. But if new plugs & wires went in, and you have spark trouble, then the ignition coil pack should be tested.

On either spark or fuel problems, check all of the wiring & connectors for ignition coil & fuel injectors. The fuel injectors can also be tested with an ohmmeter (that’s not a complete test of operation).

I think that you need a new mechanic since there is obviously something wrong. I’m not a professional mechanic, and I’ll bet I could find it.

What has helped some people with this type of intermittent problem, and it’s a very cheap, is to swap, or replace, the fuel pump relay.
The voltage to the fuel pump should be checked, and the electrical connector should be unplugged and re-plugged. The wiping action can improve poor pin connections.