That relay marked J is actually a Gottlieb AS Stepper unit. I have 2 of them on my Card Whiz and if their not working right then yes you can have all sorts of problems.

It is explained in the Marvin guide how to service this unit, but here is a quick rundown on how to test/ service it.

1. Unplug unit and use a 9Volt battery and croc lip leads onto the coil terminals and pulse it just by touching the croc clip onto  coil lug and see if it steps around all the way and doesn't get stuck.
2. Clean both sides of the little circuit board ( that has the copper tracks on it ) using very fine wet N dry paper or scotchbrite and then use isopropyl alcohol to clean off any gunk. Do only one side at a time.
3. Take off the little stepper contact and gently clean the contacts on that. When you reassemble make sure that the stepper contact is making good contact with the tracks on the circuit board. You can adjust tension on it so that it does make good contact.
4. While the unit is apart, clean the nylon ratchett/ cog assembly too using metho or iso . If its like mine then there will be dust and grease on it which causes the ratchett to stick and not move freely. These are nylon and dont usually need any other lube.
5. Remove the armature plate ( the bit that gets pulled in by the coil) and clean that too including the little nylon bit at the end. If that has gunk in it then it wont advance the ratchett properley.
6. Finally reassemble and test it again to see if it steps all the way around and if not then the spring may be cactus, so just shorten it by one or two loops so as to give the spring more tension. Do replace the spring sometime soon though.
7. While the unit is apart its a good idea to clean those switchblade contacts too using business card or wet"n"dry.
8. It should now work properley. If not then at least you have now given it a service for the first time in its life and it is one less thing that needs attention.

You can probably borrow one of these AS steppers from another EM but just be aware that there are at least 2 types, so visually inspect it to see if the one you're swapping is exactly the same.