Rare indeed... The EQ is similar to a 550A, not an A1, as the A1 was years later. The TRIM pin was related to all op-amps made in that pinout configuration, which was an instrumentation amp for analog computers, servo controls, etc. It is to TRIM the DC offset, and not used in any of the audio applications.
The gain trim resistor was for use as a fader driver or fader make up amp, it gave you up to 12 dB of gain, so you could have a preamp drive the fader, then the fader at zero position would be 12 dB down, and the EQ would make that up. Leave it off and it will be close to unity.
Their will be a little gain, as they were all designed to be loaded with a 600 ohm resistor or a 600-1K fader.
For the oscillation issue, two things. Put a 33pf cap across the output op-amp between - and OUT. also, do the same for the ICs. I don't see any caps around them. The filters are either all in series between the input and output amps, (most likely the amp in the corner input.) that does the cut, then you bypass that and move the filter into the feedback path of the amps for boost. That is where there is instability. The ICs serve as buffers between the filters so they are driven by a lo-Z source.