Hi,
Not always but often, a backfire is caused by a fuel pressure issue. Have you ever noticed any black smoke from the exhaust? Is the check engine light staying on when the engine is running? Have you checked fuel pressure?
Here is a quick video showing how to draw diagnostic trouble codes. It may be very helpful.
https://youtu.be/YV3TRZwer8k
I realize most people don't own a scanner, but often times a parts store will do it free of charge, or they will lend / rent you a scanner.
Next, take a look through this link. It discusses common causes of a backfire.
https://www.2carpros.com/articles/engine-backfires-while-running
Since you have already replaced many ignition components, I would start with the fuel pressure. Here is a link that shows how to check pressure:
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator
Here are the directions specific to your vehicle with pressure specifications. The two attached pics correlate with the directions.
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1998 Ford Mustang GT V8-4.6L SOHC VIN X
Procedures
Vehicle Powertrain Management Fuel Delivery and Air Induction Fuel Pump Fuel Pressure Fuel Pressure Test Port Service and Repair Procedures
PROCEDURES
Fuel Pressure Gauge
pic 1
SPECIAL TOOL(S) REQUIRED
Pic 2
REMOVAL
1. If fuel injection supply manifold is mounted to engine, remove fuel tank filler cap. Then release pressure from system at fuel pressure relief valve on fuel injection supply manifold using multiport fuel injection Fuel Pressure Gauge 310-012 (T80L-9974-B).
NOTE: Fuel pressure relief valve cap on fuel pressure relief valve must be removed.
2. Using an open-end wrench or suitable deep well socket, remove fuel pressure relief valve.
INSTALLATION
1. Install fuel pressure relief valve. Tighten fuel pressure relief valve to 7.75 Nm (68 lb-in).
2. Perform post-service procedures. See: Fuel Pressure Release > Procedures
3. Install fuel pressure relief valve cap. Tighten fuel pressure relief valve cap to 0.6 Nm (5 lb-in).
____________________
If you don't have a fuel pressure gauge, again, most parts stores will lend or rent one to you.
Let me know what you find or if you have other questions. Also, if you find trouble codes when scanning, let me know what they are.
Take care,
Joe
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Tuesday, February 11th, 2020 AT 6:12 PM