If interested I’d suggest Googling tape in/out (loop) and processor in/out (loop) to understand the functional differences. I’m not clear on all the differences of how the signals are routed internally and how they are manipulated but would suggest starting by using the processor in/out. Functionally, as you would use it, this is preferred.
If the images I found are correct, your preamp has a processor toggle switch on the front panel. In one direction the internal preamp section output (before volume control) is routed to the processor output. That output is routed to the input of your EQ and the EQ output routed back to the processor.
With the toggle switch in the other direction the processor loop is bypassed and the internal preamp section output goes where it would otherwise go.
Functionally I think the difference between tape and any other component input on a preamp is the addition of tape out, which simply allows you to record the selected input. For the EQ to be in the signal path of whatever you are listening to, you’d have to select Tape as your input. Without a Tape monitor button on your preamp (which, if present and with a compatibly equipped tape deck, would allow you to listen to what you’ve recorded) I’m guessing you’d still be listening to the desired device (eg Tuner, CD, Aux 1, Aux 2) but the signal path would be unnecessarily complicated and confusing.
So using the processor loop will allow you to use the input selector as you would normally use it, but provide the flexibility to switch the EQ in and out without degrading or affecting the signal path. Your EQ will have a button or switch that will bypass the EQ but it won’t be the same thing as the processor toggle switch.
Lastly the unbalanced outputs you mentioned are meant to be plugged directly into your power amp inputs. Routing these to your EQ might make noise but the input to the EQ would vary with the volume, which you don’t want. Whatever processor is used and for reasons I cannot explain, the input signal should be constant.
Good luck! While I really appreciate what modern signal processors can do, I’ve always been partial to EQs even if I had no idea what I was doing when turning knobs or pushing sliders.