My Mom used a Singer just like that for years. I loved to lay down on the floor when I was rug rat and watch all the monkey motion with the pedal and crankshaft.
David, I've played around with machine a little trying to teach myself to sew and last night it hit me like a ton of bricks. You understand ignition timing on a VW engine as well as anyone and it's probably due to watching your mom turn that rocking monkey motion of her foot and the treadle into a smoothly rotating flywheel.
I've been in the training department at work for over 20 years. My training job was teaching raw recruits how to set-up, maintain, trouble shot and repair Sulzer Projectile Weaving Machines. I learned really fast that to teach an adult something new, you had to use written instructions and letures, but without hands-on visual aids (like cut-aways) they could see and feel, they may learn to make a setting, but they wouldn't really understand the importance of the setting and that would be a huge handicap when something went wrong and they were having to trouble shoot.
Here's where the treadle relates to ignition timing. The treadle is the pistion going up and down in the cylinder. Your foot pressure is the expanding gasses in the cylinder on the power stroke. Your brain telling your foot when to begin pressing on the treadle is the ignition timing and your brain telling your foot whether to put the pressure on the toe or heel side of the treadle is the distributor putting the spark to the correct cylinder.
So you turn the switch to the start position and your VW engine starts spinning slowly in the correct direction *(on the sewing machine, that's you spinning the handwheel on the machine) . . . at the proper time, the ignition system makes a spark that ignites the compressed fuel/air mixture *(your brain telling you when to push down on the treadle just as the crankshaft crosses top or bottom dead center). The rotation of the distributor turns the rotor to the correct lug on the cap to feed the spark to the correct cylinder *(that's your brain telling your foot whether to push with your toe or heel).
If you get the timing and spark distribution just right, you get a smooth running, efficiant engine that will push you down the road with a great deal of reliability *(or with the sewing machine, you get good smooth stitches, no broken threads or needles, neat looking seams, etc.).
If you get the spark to the cylinder late, you loose power and waste fuel creating heat that doesn't do any work . . . too late and the engine just won't run *(with the machine, you get a surging rotation that makes it really hard to do good work with the bussiness end of the machine).
If you get the spark to the cylinder too early, the fireball will hit the top of cylinder and try to push it back down while the crankshaft is trying to force it back up. Getting the spark there just slightly too early can give you a little extra power, but it's coming at the cost of creating a lot of extra heat and physically damaging the engine, especially the tops of the pistions. Spend a few miles going down the highway like this and your engine will be toast in pretty short order. There comes a point when you get the spark to the cylinder so early that it just stops the rotation of the engine dead in it's tracks *(on the machine, you press the treadle very slightly too early and you can really get the thing whizzing, but it's keeping all the treadle parts under constant pressure that will cause it to wear prematurely. If you press down more than just slightly too early, the momentum of the flywheel can't overcome the pressure of your foot and the machine will instantly reverse direction . . . depending on how fast your are going when it happens, it can do anything from messing up your work (at real slow speeds) or breaking the tread and creating a tangled mess to breaking needles or worse. The faster you going when you "fire" too early or "on the wrong cylinder" the worse the mess/damage can be).
So, if anyone want's to REALLY understand ignition timing, try to sew with an old treadle powered sewing machine. You can not only see it, you can feel it. Related that to everything you've heard and read about ignition systems and some of the fog will lift, the smoke and mirrows will go away and the lights will come on.
Mom refused to covert it to a electric motor. She said she had better control with her leg and foot. I could testify to that on my backside when I got out of line. 
PS . . . David throwing a Dasher part at you when you start screwing up your ignition system is just a flashback to his mom's foot keeping him in line as a kid. It's a hard job, but somebody's got to do it!
