I've also got a 3w1 and found this thread while googling. It would be interesting to hear how you got on with your project.
In case you've not worked it out yet I can tell you how the pulses work based on what the 3w1 does (assuming it's more or less the same).
It basically works like this:
There's letters (A-V, omitting some like O or I) and numbers (0-8), making a total of 160 possible selections. When a combination of Letter+Number has been pressed, a motor moves a contact arm first over numbers 1-8. The contacts are wired in series, so if I'd press 5, pulses would be fired when the contact arm went over 1,2,3,4 and 5. Same thing then happens again for the letters, with a longer pause in between to detect the transition from number to letter.
Not quite. Yep, it starts off with a "rivet" per number (starting with 8 ), if you select 8 all will fire, if you select 1 only the last one will fire (I'm sure you know but, for the benefit of everyone else, the buttons push to break the circuit). Then there will be a strip of rivets(11 on mine) all connected (I can just see the wire behind the selector plate in one of your photos so I assume it's the same) - if these make one long pulse it is an odd letter (i.e. A, C, E etc), if 11 separate pulses are fired, it's an even letter (i.e. B, D etc). Then comes the gap (or pause as you say), the 10 "rivets" after the gap each represent a pair, so if the first rivet is fired it is A or B, the first and second = B or C....
Easiest thing to do to check the pulses without worrying about frying your Ardiuno is to wire a bulb and battery in serial, connect one end to the signal screw and earth the other. For example, If you select A1 you should see nothing, then a single short pulse, then a long pulse, then a single short pulse, if you select V8 a short pulse should fire on every rivet.
You can also use your multimeter to check the resistance between the signal screw and each rivet while selecting buttons (unit powered off but with the cam set to credit mode - means you don't need 4 hands for this).
Documentation on these machines (especially on the parts you usually wouldn't have to worry about when hooking it up to a regular jukebox) is quite hard to find, so unfortunately I haven't yet found anything about the pulse timing..
From what I can see of your photos it looks very similar to the 3w1 - the manual for that is available at www.kjq.us.com/images/3w1.pdf
Anyway hope this helps someone. Let us know how you're getting on.