1- Does the relay click during Lamp Test ? It should.
Make sure there are no cold solder joints under the header pins
and relay of the Solenoid Expander board. Bally machines of that era
are notorious for cold solder joints at connector headers, on all boards...

2- Looking at the EBD Schematics, you need four things to operate the
relay on the Solenoid Expander board:
- presence of 43V solenoid voltage going to one side of the relay coil
    on the board (pin 9);
- trigger from the lamp driver, feeding the bulb as well as the opto (pin 2);
- presence of the switched lamp voltage (pin 1);
- and presence of the mandatory ground (pin 3).

3- if I read the schematics correctly, the trigger originates from the main
   lamp driver board, J3 pin 11 (Q54). There seems to be a mistake on
   the schematics, J3 pin 11 of the lamp driver should connect to J1-2 of
   the Solenoid Expander board (and not J1-3 as printed in the diagram).

Checking the above, using the pinrepair.com reference, taking continuity
and/or voltage measurements, should easily get you back in business.

Cheers,
- Sylvain.

Thanks Sylvain.  

I reflowed the solder at the header pins. However, I ended up swapping with a fully functional board anyway and it still didn't work.  You're right...I'll just have to start checking voltages and trace back the problem.   I made a little progress, then got sidetracked.  I hope it's just a transistor on the lamp board and not a rectifier issue.  

I'll give it another go tomorrow.

Update :

Rather than track down the transistor on the Lamp board that may have been fried, I put in another lamp board that I knew was 100 %.  ( From the schematic, I believe Q54 goes to the solenoid expander relay, but I never confirmed it ).   When I swapped the lamp boards, the relay came back on line.  

Now when I run the coil test, the relay pulls in and the ball kicker and the saucer coils fire, BUT the 4-target reset coil still does not fire.

When I check the lugs, I get around 55 volts.   Just for fun, I put in a comparable coil, but it didn't fire either.  

Can't be a transistor on the SDB because the same transistor fires the #2 drop target and that coil works fine.  

I'm kinda lost as to how to go from here.  I appear to have continuity, proper voltage and good transistors but still have no coil action for that 4-target bank.

I replaced BR1 with a bigger rectifier, but TP4 is still only measuring 5.5 VAC rather than 6.5 VAC.  Could that be an issue ?  If so, why would it be so low and how do I beef it up ?

So many questions....so little hope.

Getting there!

In order to fire a solenoid, you need +54V or so on one lug
(it is present all the time on all coils providing that both
main solenoid & under playfield fuses and holders are good),
and connection to ground on the other lug (via the drive transistor
on the solenoid driver/solenoid expander relay contact).

You will need to trace the ground side wire of that 4-target bank
reset coil, all the way to/through the solenoid expander.
There is probably a missing or misconnected wire somewhere.

Unfortunately I cannot help you any further here. All the details
are in the above posts/replies and schematics. Yes, Q54 too

Do not give-up, you can do it !

Good Luck !
- Sylvain.

Quoted from sylvain

Getting there!

In order to fire a solenoid, you need +54V or so on one lug
(it is present all the time on all coils providing that both
main solenoid & under playfield fuses and holders are good),
and connection to ground on the other lug (via the drive transistor
on the solenoid driver/solenoid expander relay contact).

You will need to trace the ground side wire of that 4-target bank
reset coil, all the way to/through the solenoid expander.
There is probably a missing or misconnected wire somewhere.

Unfortunately I cannot help you any further here. All the details
are in the above posts/replies and schematics. Yes, Q54 too

Do not give-up, you can do it !

Good Luck !
- Sylvain.

"... A-hunting I will go, a-hunting I will go......"   

Thanks Sylvain.  Next time I post it will be to tell great tales of my success !

Quoted from sylvain

You will need to trace the ground side wire of that 4-target bank
reset coil, all the way to/through the solenoid expander.
There is probably a missing or misconnected wire somewhere.

Unfortunately I cannot help you any further here. All the details
are in the above posts/replies and schematics. Yes, Q54 too

Do not give-up, you can do it !

Good Luck !
- Sylvain.

ALL HAIL THE MIGHTY SYLVAIN !!  

Finally had enough.  Started cutting off wire ties and tracing the wires back from the offending coil's lugs.  Only had to go about 12 inches to find the problem.  The power wire to the coil was daisy chained from the saucer coil.  At first glance, it appeared to be making decent contact.  Then i gave it a slight pull and it came right off !  I'm both estatic and angry at the same time !  

The biggest enemy to trouble-shooting any electrical or mechanical problem is when 2 things happen at the same time but are completely unrelated !   Since my lamp board transistor that drove the relay was fried, I assumed that it had to be the root cause of my target reset problem.  Never occurred to me to bother looking for a power issue as well.

I was just about to put my EBD up for sale for $500 to any MAACA member.  But thanks to Sylvain, I didn't.      

( Oops...maybe I shouldn't have said that. )

EBD for 500$, hey remember, non-working feature on those early 80's are always much more easy to fix then we think. Only follow the logical step and you find the problem. Very often it's a problem from bad contact or damage wires because of rust or a transistor very easy to change.