Section 1-4 of your manual describes the operation of the brake and capstan solenoids. It might be nice to have a scope to check for the 200 mS 24 volt flashing current but a DVM will work for the 12 volt holding current.
Troubleshooting is a process of dividing a circuit in half looking for the point where coorect operation fails.
Looking at figure 1.5(B) (page 58) I see U519. It shows play in and play as two signals that you can test for. If play (pin 12) is high and the solenoids do not work then the solenoid circuit is bad. Otherwise the problem lies in U512 or the circuits that drive U519 pin 1(play in).
Does the brake solenoid actuate? If it does then we can deduce that play goes high and that the problem is with the capstan solenoid circuit.
When not in play (stop mode) the collectors of Q538 and
Q541 should both be at or near 12 volts. When in play mode they should be at or about 0.6 volts. These transistors turn the solenoids on and off. If no 12 volts then you have a bad 12 volt supply or an open solenoid.
The cathodes of D515 and D516 should both be at about 12 volts. This should be true in any mode (play or stop) Their job is to short out the voltage spike that happens when you stop current to a solenoid coil.
When you enter play mode from stop you should be able to measure the 24 volt flashing current that is applied to the solenoids. It is there for only 1/5 of a second so you meter would not record 24 volts but rather something higher than 12 volts then settle down to 12 volts.This may be easy to see or hard depending on your meters reaction time. Of course a scope shows this quite nicely.
The flashing current causes the solenoid to actually move and the holding current keeps it actuated (more power to actuate than to stay actuated).
Hope this long winded post helps.
--Ethan