I have a 1988 Buick LeSabre, 3800 V6 engine, with a no start problem.
Despite it's age, it's probably in better condition that some 5
year old cars on the road. It stalled out 3 times on a recent trip.
After waiting 15-20 minutes, I could get it restarted but it ran rough,
had to keep on the gas and stalled out shortly thereafter. I had it
towed home and the next day it started OK, ran for 15-20 minutes at
idle then died. Same thing the next day. Definitely a repeatable and
heat related problem.

When I try to restart it, it will crank over a few times, then fire,
but not continue to run. No trouble codes are ever set. I can hear the
fuel pump running when I turn the ignition on. Fuel pressure is
constant at 45 PSI.

A test light connected to a fuel injector does not flash when the
engine first cranks over a few times but will start to flash when the
engine fires. I understand that the ECM will switch from simultaneous
to sequential injector operation at 400 RPM with cam sensor input..
Does this explain what I'm seeing?

I also disconnected the wiring harness to the fuel injectors and
checked for spark on the 3 coil units with a timing light while I
cranked the engine. Seemed to be OK. Secondary coil resistance is about
12K on all 3 units. I've had coil packs fail before, but not with
these symptoms.

Are these symptoms of a crank sensor? A scan tool shows engine RPM
while cranking. At the crank sensor connector I do have power and
ground. I also repeatedly grounded the 18X signal input to the ICM with
the ignition on and got the injectors to fire and fuel pump to
activate. What about the sync signal input? What purpose does it serve
and how can I test this?

I've been thinking of borrowing a scope from work and backprobing
some of the input signals to the ICM. Is there anything else I should
be looking at?  If I do need to replace the crank sensor, how easy is
it to remove the balancer? I did not see any holes for a puller once
the retaining bolt is removed.

Thanks in advance for any comments!