5-40 is the size.

Or you could buy these...
ebay.com link: Gottlieb 1975 300 Pinball Machine set of 4 score reel units

and have a variety of parts

http://www.pinballspareparts.com.au/4405-01117-00.html

Should be a 5/16" size

Damn I wish we were metric....

I believe it is a 3/16" size, not 5/16".

Mcmaster carr shows all of their 5-40 nuts @ 5/16, except the special small nut

Now I have to try one. I recall using the black handle nut driver from my Sears set and it is 3/16". I need to tonight when I have a game in front of me.

How about both?

https://www.amazon.de/dp/B01MRU9CZ1/ref=cm_sw_em_r_mt_dp_e-tSzbK1E1CVM

or all

http://a.co/jh3ahNc

or these:
ebay.com link: 14x Power Nut Driver Hex Schaft Bohrer Adapter Socket Schraubenschlussel Tool

or these:

ebay.com link: 7 Piece SAE Nut Driver Set 1 4 3 16 11 32 5 16 3 8 7 16 1 2 SAME DAY

personally, I'd get the craftsman. You can always just take them back to your local Kmart.
ebay.com link: Craftsman 10 Piece Nut Driver Set Set SAE Metric

Here are sets of "spanners" that you would find interesting.

ebay.com link: Craftsman Wrenches Ignition Open End Steel Chrome 1 4 7 16in SAE Sizes Set of 8

ebay.com link: Craftsman 12pc 6pt SAE Wrench Set

Spanner.

Warning lights are flashing down at Quality Control
Somebody threw a spanner and they threw him in the hole
There's rumors in the loading bay and anger in the town
Somebody blew the whistle and the walls came down
There's a meeting in the boardroom they're trying to trace the smell
There's leaking in the washroom there's a sneak in personnel
Somewhere in the corridors someone was heard to sneeze
Goodness me, could this be industrial disease?
The caretaker was crucified for sleeping at his post
They're refusing to be pacified it's him they blame the most
The watchdog's got rabies the foreman's got fleas
And everyone's concerned about industrial disease

I could put a few score reels up on ebay if you like. I'll do the international shipping thing and ebay handles overseas shipping. It may cost you, I don't know. I do know that after being a nice guy a few years ago and sending a "free" part to a pinsider in Canada, I ended up with about a $15 shipping bill, filling out customs forms and 45 minutes at the post office, so I'm done with that.

Not sure what your long term intent is, but IMO, one of the biggest mistakes I made early in the hobby was sourcing/buying new things like this nut, when it is easier and cheaper to have some spare assemblies around.

I looked at both an Outer Space and a Jungle Princess and the driver size for the factory nut on the score reel end of stroke switch screw was 3/16".

I did not check in any way but looked like the screw could be a 4-40.

I think you are right, Mike. I think the 5-40 is for the relays. These are smaller.

Actually, that should be typed as 1/4, 3/16, 11/32, 5/16, 3/8, 7/16, & 1/2 It's fractional from an inch.
Why do you need smaller sizes? I don't recall ever seeing any nut smaller than 3/16" used on a pin.

I agree with dasvis. Where do you need a size smaller than 1/4"?

Switch stacks are normally held on with a slotted head screws.

Do you have pictures?

I'm guessing the switch stacks on the score reels.

No idea how small they are. You can measure them yourself, right? Take the number in mm and divide by 25.4 to get inches. Then multiply by 32 for the size in 32nds of an inch. Reduce the fraction to 16th of an inch if required.

Example 1 5.6 mm /25.4 mm/in * 32 = 7.055 or 7/32"
Example 2 4.8mm /25.4 mm/in * 32 = 6.046 or 6/32" but WAIT, that fraction can be reduced. 3/16" (which is what I think it actually is)

Anyway, a nut driver is not my choice for this application. I prefer ignition wrenches or usually, just a needle nose plier or my fingers. You often need to get in from the side.

ebay.com link: Vintage 18 Piece Oxwall Combination Ignition Wrench Set USA Made

ebay.com link: VINTAGE CRAFTSMAN 10 PC COMBINATION IGNITION WRENCH SET MADE IN USA