Interesting combination of posts in this thread. Three different models (at least one each, 760, 740 and 780) with an intermittent no-crank that can be bypassed by engaging the solenoid from under the hood. They are distinctly different main harnesses. In fact, the 760 has its fuse and relay panels in totally different locations than the other two cars. Oddly, they're all 1989 models.

Apparently, I'm the only one that took the time to properly troubleshoot the problem with a voltmeter, and not simply start replacing parts. Remember, I cannot tell you what is wrong with your car - only what was wrong with mine. From an old car disclaimer - "your mileage may vary".

My car had the trouble of "faint click" instead of starter engagement for over two years, sometimes months between events. First, it was most likely (but not always) when very hot, such as after a short stop during a long trip. I suspected the usual; battery cables, starter solenoid or brushes, neutral switch, dirty connection somewhere. Then it was happening more often and occasionally when cold. I got tired of getting the sleeves of nice shirts dirty while reaching in to jump the terminals, so I connected a length of AWG16 to the Green pushon terminal at the solenoid and tied the wire near the battery so I could touch the other end to the + clamp when the car wouldn't crank. This made the problem less inconvenient.

Finally... it happened at home, in nice weather, and I had some time before I needed to leave for work. My opportunity to find the answer and be done with it.

Grab the voltmeter and connect it to cheater wire. Aha, only 8 volts to the solenoid in start position. Battery still reads over 12. Only two possibilities here; the solenoid is taking much more than design current (8-10A in operation, 18-25 for pull-in) or a current loss somewhere between the ignition switch and the solenoid. The 0.2 volt drop on battery voltage when turning the key from run to start position told me that the current draw was low, not high. Hoping it might just be the underhood connector to the engine harness, I found the green wire where it leads into the firewall (before the connection to engine harness) and punctured the insulation for a voltage reading - still low. Down comes the lower dash :-( I dug for the alarm wiring first, since add-on circuits often cause troubles. I got about 11.75 volt in and out, meaning alarm and ignition switch were definitely not the problem. Voltage there was the same when moving the shifter out of park, meaning alarm was wired ahead of the console, so I spent 45 minutes hunting for the easiest access to the neutral interlock switch with minimum disassembly of the console (I'm the one with the 780). The connector on mine was eventually located jammed under the carpeting and held tightly by the bolted side panel of the console. Of course, it could not be tucked someplace accessible. Did all that digging pay off with an answer like a bad neutral switch or dirty connections - NOPE. Still more than 11 volts in the start position. That wire from the interlock winds through the dash and goes next to the humongous 53 position connector tied to the dash brace above the hood release. Metal strap, wire ties, located out of sight - connector finally down enough to dig in and find that fat green wire. Damn, 11 volts there too. I probed into the insulation of the wire leading toward the engine harness and got the same reading.

So there it is... 30CM (a foot) of wire, with 11 volts at one end and 8 volts at the other. Just replace it you say? Not only is that wire bundled in the densest harness in the car (injection CPU is second), but it has to pass through the firewall to meet the engine harness. Watching the meter while moving the defective section of harness did not help to locate any specific area of the harness that was bad. I'm not the type to make repairs with shortcuts but in this case, moving the current load off of the failing circuit and to an underhood relay made the most sense - considering both labour/time, and likelihood of a trouble-free repair, not just an improvement.

My attack.... Disconnect battery (find radio code first if you have a later head unit). I made a simple harness with two 16 gauge wires long enough to run from the starter solenoid to the brace above the power brake booster, near the engine harness connector. I wiretied it to the factory engine harness for neatness and protection of the unfused power wire. The lower end of the wires: one has a large ring end (I think it was 8MM dia) to fit the top stud. That was placed on first so it is clamped tight by the battery cable. The other wire has a covered pushon to fit where the original green wire was. The top ends connect to pins #30 and #87 of a Bosch 30/40A cube relay that I mounted on the underside of the corner brace to hide and protect it (either wire to either pin). I cut the original green wire near the relay and also made a short ground wire to connect to a body bolt. These two wires got covered pushon terminals and go to #85 and #86 pins of the relay. Same for these.... either wire to either pin. Double check wire routing and reconnect battery.

What I did not do; because it would take different tools (a scope, or at least an analogue voltmenter) to catch the voltage drop when the starter did engage properly, I did not take that reading to determine whether the wiring carried full current during the instant before pull-in, or (much more likely) the "normal" operation was just barely enough for pull-in, at which point the needed current drops to less than half, keeping starter running dependably.

The bottom line: Get a length of 16-20 gauge wire with both ends stripped back an inch. Remove the green wire from the starter and stick one end into the female connector. While holding this together, push it onto the male (blade) terminal of the solenoid so the wire strands are stuck into the joint. Tape the other end of wire so its bare end is accessible but cannot hit bare metal. This will be your test point. When the problem occurs and the starter does not engage, connect a voltmeter set to 20 volt DC scale; red wire to your test point, and black wire to battery negative post or ground. Position meter so you can see it from driver's seat, and then turn key to start position. If there is more than 6.5 volts - your failure is a current loss in the circuit and not an open switch, alarm relay, or broken wire. Adding a relay close to the starter is an appropriate repair. Before anybody pipes in with "6.5 volts is not good enough to drive the relay", remember that this is normally a 15-25 amp circuit drain in this mode.

If you got zero or almost no voltage - take the red meter lead off the test point and touch it to the battery + post to confirm your ground connection and meter operation. If the meter works and your voltage is still very low or missing at the test point in start position, your problem is different and must be diagnosed methodically. You'll need to confirm ignition switch output voltage at the pink wire to the neutral switch, and at the green wire after the neutral switch to locate the defective or misadjusted switch.

The above test will not tell you exactly what is wrong, only whether you have a condition that would be cured by adding a relay.

My thoughts... I was able to narrow my car's problem down to a section of wire in the main harness, and I eliminated connectors and ends as a possible cause. Flexing the harness made no change and the wiring diagram shows a continuous wire. The wire was failing in some way over time, as my own car worsened over a period of two or so years. It is possible that the strands are becoming fusible due to the current demands and reducing the effective wire diameter. If it was a design issue, other years would be affected. My own suspicion is that the Green wire used to assemble all three (different) harnesses, possibly in different factories, was supplied by the same vendor and is defective either in alloy (the progressive strand failure is not uncommon with copper-clad aluminum wiring), or simply lighter duty than specified. Since I do not know for certain that the other cars even have the same failure (they only have a similar symptom), this is only a guess. The possibility that repairing one section of harness might cause another section of the same wire to fail under original load in the future was one of the reasons I chose to modify the circuit with a relay.