Help needed: 4kq engine still cuts out

[Jpinkowish at aol.com]

Hi folks,
The engine is still cutting out.
Here's what happened yesterday:
--turn ignition to "on"(not crank), still get a tach bounce 0-->1k-->0
--Start the car(no problem) and idled for 20 min to normal operating temp.
--shut down, restart a cuppla times, no problem.  still getting the tach
bounce.
--shut down, 2 hours later, drive 30 miles on local roads/freeway no problems
--4 hours later start drive home.  sitting at light after driving 3 miles,
tach bounces from 1k-->2k with no increase in engine speed.  drive on highway
for 15 miles, exit, shift into neutral, and engine dies about 5 sec later.
--sit for 2-3 min, switch ignition to "on"(not crank"), get tach bounce, and
starter briefly engages, then lets go.  I think that this is key info.
--get car started and continue home, with engine dying about every 3
miles(about 3-4 min).  keep getting tach bounce, and once more the starter
tries to engage with the ignition in only the "on" position.

Now, I will admit that I've been having a sporadic problem with the solenoid
not engaging the starter motor.

So, questions I have(without yet going through Bentley):
--Something in the starter/solenoid shorting out and grounding the ignition?
--Ignition switch problem?  Harness plug looks clean, wiggling the key with
the engine running does nothing.
--Hall sender in distrib?
--Ignition control module?

What baffles me is the time and/or temp(?) cycle of the cut out.

I wish that the engine would croak in the garage!

Suggestions are much appreciated.

Jan Pinkowish
'85 4ksq
Bristol, CT