I had a TEAC reel to reel tape recorder, which had an autotransformer multi-tapped primary. The reason being that the spool motors were fed different voltages depending on its actual function:
1-During play or record, the take up spool motor would receive about 75% voltage, and the supply spool motor about 40% voltage, to maintain tape tension across the heads. The tape speed was of course, regulated by a synchronous capstan motor.
2- During fast forward or rewind, the take up spool motor (could be either side) would receive full line voltage, whereas the other motor would receive about 25% voltage, again to maintain some lower value tape tension.
Of course, you had the multiple secondaries to supply the required electronic voltages. You do not mention whether this tape machine was tubed or transistorized. If tubed, a pair of secondary wires (green-???) were the heater voltages and the remaining could be different V+ voltages.
But again, all of this is speculation. Proceed with the valuable advice from the previous posters.
The *incandescent* bulb in series is a good trick to prevent a severe short circuit. If it lights very dimly, you are fine. OTOH, if it lights brightly, you are overloading that winding. I have used 25 or 40 watt bulbs for that purpose.