Sounds like an early 6803 game? Eight Ball Champ?

The displays have BCD (binary coded decimal) data coming in on 4 wires. That signal goes to the 4543 decoder, which then figures out which digit to light. To be more exact, the 4543 has outputs for each individual segment (ie. "A", "B", "C", etc).. so when the 4543 receives the BCD data as inputs, it then turns on or off individual segments outputs based on the BCD (you can view this in the 4543 datasheet). The segment outputs are then connected directly to a segment driver transistor, which acts as the switch to ground.

Have you checked continuity between 4543 pin14 and Q19. Then on the resistors & their connection points, including pin38 at the plasma display glass? Here's some schematics if you need them.. https://www.pinitech.com/retrofit/schematics.php

Was the segment previously working before the solder blob incident? Is the G segment on every digit of the display non-functional? Also, does it appear darker than the other segments when the display is unlit?

In display test, do all digits cycle numbers otherwise and is it just the G segment out on every digit? Or do you have other issues?

In terms of the darker segment, I'm not sure exactly how an individual segment might fail in a display.. if enough current hit it, it'd probably have gone "super nova".. lighting the segments affected almost pink for a bit and likely damaging or burning the G segments out completely. If it's got a burn mark/dot on the segment on some or all digits (depending which ones were lighting up while the short occurred), then they may be burnt out. If the G segments are just a bit darker or as dark as other segments, they may be ok.

The G segment is going to go to a single plasma display pin.. and then into the plasma glass. I guess another failure mode would be the thin wire inside the display glass for that segment to have taken all the current and blown open. Not sure if you'd be able to see anything on the glass itself. Otherwise, I'd imagine this short occurred while the game was in attract mode.. and only a few digits were being enabled... in which case, if you currently have NO "G segment" lighting on any digits, that may still indicate there's a problem before the display glass. Of course, with replacing the 4543.. and the transistors.. you start narrowing down possible culprits. Continuity between things in that circuit can be checked according to the schematic. You can check the resistors too. At some point it may come down to the plasma glass as the remaining possibility.

Not sure where you're located since it says "Unknown" for location, but you're welcome to try one of my 6-digit LED displays if you're within the U.S. It should blend well with your existing plasma displays, but I'd let you be the judge of that. And I'm currently offering a 2wk return / refund (minus shipping costs) on purchases of single assembled ORANGE displays for new customers of them... that way people can try them and see how well they mix with plasma displays in their game when just replacing a single display or two. LMK if you're interested and we can set something up

https://pinside.com/pinball/forum/topic/new-pinitech-led-displays-for-classic-bally-stern-plasma-contender

Looking more likely that's the case. The segments for each digit should be internally wired together in the plasma glass. There's only a single pin bringing in each segment.. so if the segment is lighting on some digits, that would seem to indicate a plasma glass issue. Usually if it's the segment driver circuit that's the issue, you'd have all segments on all digits with the same problem.

Comparing the right most 4 digits "G" segment to the left most 2 digits, does the G segment look darker/burnt?

It's interesting if the short took the right most 4 digits out.. if the game was in attract mode. It looks like it should only be the 1st, 2nd and then the 4th, 5th digits (skipping a number in-between) that would have been enabled on that display at any given time (to light the credit/match numbers). I'm surprised it wouldn't have just taken out the G segment on the digits lighting the credits since that's what would typically be lit up in attract mode. That said, I think the internal plasma glass wiring is a bit different than an LED display, so maybe the current was spread across the first few digits wired directly from the plasma pin for the G-segment and they burn out right to left