If there is a self resetting circuit breaker (and I am not sure there is);

A self resetting circuit breaker has a bi-metalic strip inside it. When current exceeds the limit, the bi-metalic strip heat and deflects. This trips the breaker. When the bi-metalic strip cools, the breaker resets.

(a bi-metalic strip consists of two different metals bonded together. The two metals expand at different rates when heated and this different expansion causes the strip to bend)

There wouldn't be a factory installed circuit breaker in your machine. My guess is your short is somehow releasing the hold relay essentially cutting power to the game. Pressing the left flipper reinstates power to the machine through the hold relay. A lot of Ems have the left flipper button do this. You flip the power switch on and have to hit the left flipper or start a game to power the machine up.
Alex

Sometimes if your Lock relay is dirty or makes poor contact, drawing heavy current elsewhere can cause it to lose it's lock. This would present in the way you describe.

Lock or hold relays release when a player tilts the machine. Renergize when another credit is used. There may be other reasons, but that seems like a good reason to have it function properly.

This is normal. Also if there are credits on the machine or it is set to free play pushing the credit button should turn it on.

Check out these sites, they should help you out with your understanding of em pinball machines. http://www.pinrepair.com/em/index.htm
http://www.pinwiki.com/wiki/index.php?title=Main_Page

You actually can adjust the switches in the lock or hold relay to be permanently engaged. That way you would turn the power on and the machine would be "on" right away. It's a hack that you can do if you have a smoked hold relay coil. I think most prefer keeping it operating as originally intended though.
Alex

Although it's a little confusing to work through sometimes, EM games are mostly just a lot of AND and OR gates. Once you realize that, following through the logic is pretty much the same as for modern digital electronics.

On most Bally and William games, it does two things.
One de- energise the game over trip RE and Two turns the GI lights on.

there are many thread on this site about it, just search lock RE.