HOW TO CONNECT A ONKYO TX NR535 TO AN EQUALIZER

First this solution will be fraught with potential problems:
1. There is no simple monitor outputs and inputs on the NR535.
2. The NR535 analog inputs/outputs are unbalanced, where the Behringer EQ is completely balanced (TRS or XLR)
3. Insertion of the EQ is analogous with inserting an effects device in an audio loop which in the case of analog surround will cause de-correlation or the companding sidechain making for non-compliance/performance issues.

OK, now the solution can be as follows:

Since the NR535 has a Zone 2 channel, you can use these L/R RCA outputs to make an effects loop. To do this you will need to make or buy RCA to TRS (1/4" phone Tip Ring Sleeve jacks) that you will connect from the Zone 2 outputs to the CH1 and CH2 inputs of the EQ. You will need another pair of the RCA to TPS to connect the output of the EQ back to one of the RCA analog inputs on the back of the Receiver.

Now once this is done, you will be able to Map Zone 2 input to any of the inputs other than the one you are using for the output of the EQ. Let's say you have mapped Zone 1 to your gaming station. This will patch the audio from your gaming station into the EQ and back into your previously connected analog input. At this point, you can leave Zone 2 and select your analog input which is your EQ output, which is your Gaming station. If you don't have any output, you may need to go back into the Zone 2 setup and adjust the volume level.

When you don't want the EQ in the signal chain, just select the input source other than the input used for the EQ's Zone 2 output.

I am not sure if this will work for all situations as you may have technical conflicts between analog and digital audio on some inputs. In any case, this will work with analog signals and I don't see any other simple solution for your case.

I hope this solution can help.