Eureka!
A great gremlin hunter, Jim, a troubleshooter from co-owner Lionel's stationary diesel electric company, has driven a stake through the heart of the electrical gremlin aboard Hali.
Jim may have exposed problems C34 owners can create for themselves when they replace old electric fuel lift pumps with new "electronic" fuel pumps like the popular inexpensive Facet Purolator "Posi-Flo".
Later, I may write this up more succinctly and accurately. Meanwhile, brick bats are invited.
The theory -- possibly somewhat proven by the fact that Hali now starts "first time every time" -- is that a gremlin lives in the intermittent making and breaking of the electrical circuit through the "electronic" fuel pump but that this gremlin expresses itself in the rather inscrutable way of interfering with the energizing of the preheat solenoid that completes the glow plug circuit.
To paraphrase partly John's post above of June 19: on the M-35B engine wiring diagram [see your Catalina owner's manual] and in the actual wiring of the M-35B engine, when the engine is not running the electric lift fuel pump will only operate when the keyswitch is in the "glow plugs on" position. Put another way, the electric lift fuel pump on the M-35B will operate (a) when the keyswitch is in the "glow plugs on" position (which of course it only should be before the engine is cranked) or (b) when the low pressure oil switch is closed (as it usually is once the engine is running). The fuel pump is wired simultaneously into two circuits - this is much clearer on the wiring diagram which unfortunately I do not have before me at the moment. One of these circuits is completed only when the keyswitch is turned to the "glow plugs on" position and one is completed when the low pressure oil switch is closed. If the keyswitch is at the "on" position but not at the "glow plugs on" position, and the engine is not running (and therefore the low oil pressure switch is not closed), the fuel pump will not be energized. (I say energized rather than operating because there will be cases when the pump is receiving an electrical current but is not operating because the fuel line pressure is such that no demand for fuel is being made - that is, I guess, above about 4 pounds per square inch gauge pressure on these Posi-Flo pumps which are rated for 1.5 to 4 PSI.) In other words, when the M-35B engine is off, don't expect to hear the fuel pump clacking away when the keyswitch is only at "on".
Now the problem as it is theorized to be is that because the electrical circuit ("preheat solenoid activating circuit") that energizes the preheat solenoid (which acts as a switch to close the glow plugs circuit) runs through the electric lift fuel pump (a clever way to make sure that when the glow plugs are energizing fuel is also being delivered by the lift pump to the fuel injection pump for onward delivery to the cylinders when the engine cranks), if the lift pump electronics are making and breaking they make and break the preheat solenoid activating circuit with the result that the preheat solenoid does not close - or closes intermittently - and the further results that the glow plugs do not energize sufficiently to heat the cylinders and compression ignition is not achieved.
Without the benefit of investigation, the speculation is that the old electric lift fuel pumps operated without making and breaking the electrical circuit and so did not interrupt the preheat solenoid activating circuit -- but the new "electronic" pumps do or can in some cases (Hali's apparently being one).
At first blush, Jim thought there was an easy complete fix: ground the preheat solenoid energizing circuit immediately after it passed across the preheat solenoid low power terminals -- that is, ground one of the preheat low power terminals and terminate the "glow plugs on" circuit from the keyswitch and the 10 amp circuit breaker/fuel pump/low pressure oil switch circuit on the other preheat solenoid low power terminal. However, on further thought, he realized that if this were done, there was a possibility, when the engine is running and the low oil pressure switch has closed its circuit to the electric fuel pump, that that circuit would activate the preheat solenoid and cause the glow plugs to energize. His more complete solution is to re-wire as indicated but with a diode (one way electrical current flow device) in the fuel pump/low pressure oil switch circuit just before it connects to the preheat solenoid low power terminal. The diode would prevent electrical energy from flowing from the fuel pump/low presure oil switch circuit to energize the preheat solenoid and glow plugs when the engine is running - something that could cause the glow plugs to crack and shed material into the engine cylinders.
Jim is going to wire the diode and send it along for installation in the circuit.
Here lies a dead gremlin (?) and maybe a stillborn one.
My many thanks to all of you who helped along this path.