Do you know what ECU this car is equipped with? The pink label 561's have mostly been replaced by this time with the more reliable white label 951, but occasionally a pink 561 shows up. They are troublesome and the problem is sometimes addressed by the work around you found with jumpered fuses.

It doesn't necessarily mean the ECU is bad. There is a red wire attached to the positive battery post that goes to a fuse mounted on the driver's inside fender and from there to the fuel injection relay above the passenger's feet.

If the connection at the battery suffers from corrosion you might need to clean things up including removing the 10mm nut that holds the wire in place.

The fuse is a trouble spot as well. Many people have replace the fuse holder with one suitable for a marine application. A cap closes off the fuse from the underhood environment.

Randy