Except mine is not class II. I did learn about appliance classes, so thanks for that! Mine does not have the double square symbol printed anywhere on the sticker, impressed into the body, etc. (I should probably get a new toaster...) I won't cut the power cord open to verify, but the other indicators are missing.
Man, you're absolutely right - I made a blunder up there (duh! Sorry, gonna chalk that up to the crummy week I've had.) - you cannot be shocked by touching both ground and hot (that's the whole thing it protects you from...) - if the ground is properly isolated/connected throughout. That was my fault. If there's tingles, no, it's not properly connected somewhere. You're right that you will not be injured, however, you will be tripping the breaker if the braid comes into contact with something odd.
Here's the thing, the inside of a bingo door contains two stacks of switches. There's also a coin mech. The outside of a bingo door contains two buttons - red and yellow. Depending on the year, they were either plastic or metal. The metal ones have a non-metal covering/end that actually presses the switches (I don't know what kind of covering it is - it is black and feels like rubber). There are also heavy-duty switch insulators there, too. It does depend on the vintage.
What can short? The switches could short if the insulator fails. The switches could short maybe somehow if the button was destroyed inside the coin door... what would happen? Well, if the insulator fails, then you will get a quicker press of the start relay, or your 50V fuse pops.
If the button insulation fails, then it's theoretically possible you could be shocked.
Ditto for the coin return button. There's a coin lockout relay which sits under the mech. If someone clipped a lead and didn't tape it, then the coin return could shock you.
If the ground braid/strap is installed inside the coin door and attached to the button inside (that'll be a trick, [the inside of the button mostly sits in a small routed channel] but doable) then yes, you would be prevented from a risk of a shock.
So to recap, a ground will prevent risk of shock. On a woodrail bingo with three metal components... I find any scenario to be highly unlikely that would cause a shock. I realize that it is protection against the outliers.
P.S. sorry for the delay in responding - I was playing my deathtraps.