I checked and I can't find a module on a 1996 3.8L cougar they have one on a 1995 by the bellows close to air intake.
I think the camshaft position sensor and the crankshaft position sensor on the lower right front of engine are your problem. If you have an ohm meter with the units disconnected and the ohm meter on the two contacts it should go from zero to one when somebody cranks the engine. I would try the camshaft sensor first.