Jake, the first step is to become familiar with the machine's assemblies. The unit that controls scanning are the two coils shown here:
http://s1192.photobucket.com/user/Rob-NYC/media/Seeb%20TSR_zpss5qcoprr.jpg.html?sort=2&o=
The coil at the right pulls in briefly when a selection is made. The one at the left subtracts each time the mech scans to the right (viewed at front). There is a set of contacts under the readout block that rides up on a ramp and closes the contacts that actuate the subtract coil.
A few words of advise; tinkering with these machines can be dangerous to both you and the machine.
I suggest obtaining a service manual whether from Victory Glass, Always Jukin or some other source.
You'll get more immediate and comprehensive responses at groups such as:
http://jukeboxaddicts.proboards.com/
https://groups.yahoo.com/neo/groups/seeburgjukeboxinformationclub/info
If the amp and selection receiver have not been rebuilt in the last 20 years, particularly new capacitors, it isn't safe to keep trying to use it as you risk doing serious damage and ruining costly parts such as transformers.
The mechanism requires comprehensive lubrication and contact cleaning. You should asses your own skills and determine how much you want to handle vs. how much, if anything, you want to send out to others technicians.
Rob-NYC