I did some checking today as I was driving around. With my ears, I have
great difficulty hearing the clicks, so I just reached under the dash, and
felt the clicks on the relay as they occurred.

The first click of the Main Relay is DEFINITELY a double-click. The others
are single clicks.

The click sequence appears to be this:
1) Turn ignition on, both relays close, one very close after the other. The
first click is harder than the second
2) 2 seconds later the Engine light goes off, and a hard click as the
second relay pops open and the pump stops
3) Start cranking, and a final soft click as the second relay re-closes and
the pump restarts.

Therefore, the third click happens BEFORE the engine fires, not AFTER.

The problem with the relay when there is no third click is that the engine
is running on the residual pressure within the fuel rail from the 2-second
precharge time before the starter was engaged. Once that pressure is gone,
the engine stalls.

So, a revised sequence:
----------------------
Driver turns key to ON (but not to START):
------------
1) Ignition switch terminal IG1 sees power. Injectors allowed power from
Main Relay term 1 (batt) through term 3
2) Power sent thru IG1 to term 5 to a permanent ground at term 2
3) First relay is activated as current flows from 5 to 2. ECU monitors this
flow at 2, but cannot shut it off. First relay is now powered ALL the time.
4) Closure of first relay will allow activation of second relay (fuel pump
relay) from term 1 to term 8
5) Before current can actually flow and activate the second relay, ECU must
supply ground to term 8
6) Grounding 8 causes both first and second relays to close

***BOTH RELAYS CLOSE AT SAME TIME (DOUBLE-CLICK)***

7) Current from term 5 is tapped from BEFORE the first relay to flow
through the closed second relay to ground at the fuel pump from term 7.
This is the fuel pump's ONLY power source, and is available ALL the time
from IG1, since it is tapped BEFORE the relays.
8) Since engine is not running and ignition has just been turned on, ECU
cuts ground to 8 after two seconds allowing just enough time to
pressurize the injectors. Second relay pops open and fuel pump shuts off

***SECOND CLICK***

9) ECU knows the engine is not running because of the Crank Angle Sensor in
the distributor, which it uses to see engine RPM.

Driver turns the key to START
-----------------------------

***(THIRD CLICK)***

10) IG1 terminal at the ignition switch remains powered as ignition switch
is rotated to START. This is necessary otherwise injectors would lose power
11) ST terminal at ignition switch is now powered, and is allowed to
activate second relay directly through term 4. ECU holds ground at 8,
cureent flows from 5 to 7 and pump runs
12) There is a redundant activation feed to the second relay during
cranking, one from 1 to 8, and one from 4 to 8. As starter is released, it
stops powering the second relay. The second relay reverts to being powered
solely by batt from term 1 to 8, and will remain this way as long as the
engine is running.