The Pre/Power jacks are the last connection in the signal path before the input to the power amp stage. The signal there is controlled by the volume control and the other signal shaping controls upstream. Equalizers are
usually used in a "Line Level" portion of the signal path, like the Tape Monitors and Adapter connection. Those "Line Level" connections are upstream of the Tone controls, High & Low filters, and Voltage Gain stages. The SX-1250 schematic shows the Line Level as 150mV RMS at the Tape Monitors and Adapter jacks. Feeding the Equalizer with the Pre outputs
may overload the inputs of the Equalizer. Certainly, people have used Equalizers in that location successfully. So the real answer is 'it depends' on the equipment. Look at the User Manual for the EQ device and see where they want you to connect it.
But 'where should I use it' is a different question than 'why is it not working'. Though they may be related.
The EQ may have a Tape Monitor loop on it as well, many do. If the EQ is not set correctly it may not be passing a signal to its outputs. The Adapter connection is not quite the same as a Tape Monitor connection. You did not specify the exact model of your EQ so I could not look it up.
The Adapter Out should go the the EQ input, and the Adapter In should connect to the EQ output.
You can test your cables with an ohmmeter, or use them in place of the jumpers to see if they pass signal correctly.
Have you tried the EQ on a different Amp? It seems to me that the SX-1250 is not the problem. The EQ may not be perfectly calibrated to have no effect on the overall level when it is engaged, that is not unusual either. Sometimes there is a level adjust on the front, on the back, or internally to match level in to level out, with the EQ set flat all the way across.
Forgive me if I am repeating things you already know, just trying to be thorough. I can be pedantic at times

. . . but I want to help.