This really is the ultimate guide;
http://www.twistedslinky.org/~link/Electro%20Mechanical%20Arcade%20Game%20Repair.htm

Typically, I will go through every stepper, score motor, score reel and switch if a machine that has been sitting for a long period of time.

It's actually good news that the game resets. The ball kicks out too?

There is no "secret" to fixing an EM if they've been sitting. You'll see many posts in the EM sections where the issue can only be found by the guy standing in front of the pin (chewed wiring harness etc.). Not to say there isn't top notch help found on this site. There are some very sharp people here that are willing to spend their time to help others.

You just have to take the time and make sure everything is operating properly visually, usually done with your hands to actuate the assembly without power on the game. Taking the time to do this will result in a rock solid player.

If the ball does kick out and you hit a playfield switch, trace that switch through the schematic. Is it any switch, pop, kicker that causes this issue?

I have an Aztec as well. It's a fun game and William's of this era also provide plenty of table speed. While not a hard pin to rack up points, spelling A-Z-T-E-C and lighting the special isn't an easy task to complete.