You're probably not going to like this...
I don't like that thing. Take a look at a Wavetek 111 and you'll toss the t hing in the trash. But that is not the point. The point is getting it strai ghtened out.
I would pull the batteries and just refit the regulator a bit. That is the stupidest power supply I have seen in a long time. Of course sometimes I ha ve to remind myself I was nine years old when it was built.
Could I do better ? I sure as hell could on that power supply. How hard is it to take a couple of diodes and make it so it will run with dead batterie s. And man, ;when the batteries are good, itt won't. Look at it. the regula tor is a single ended current source and the thing always runs off the batt eries. If it runs with dead batteries they are bad. Look at the circuit, co nstant current into a dead battery should only put low voltage across it.
You have several options. I think the best of them is to just stick a coupl e of Zeners in there. The supply shows -33 and obviously +12.5. That is 45.
5 volts. All the current comes through that 523 ohm resistor. That comes ou t to a hair less than 87 mA. That, times 12.5 volts is 1.09 W.
So take two 12 volt Zener diodes and wire them where the batteries used to be. Get five watt units to be on the safe side. If you want to get picky an d really must have 12.5 volts instead of 12, which SHOULD not matter, stick a 1N4007 in series with each Zener. Observe polarity, when you do stuff li ke that it can be easy to make a mistake and not have anything there. It go es the opposite way. But figuring about 0.7 V at 87 mA, (if that) you don't have to worry about their disspation. No matter what, I would say get the diodes from the same batch so the voltages are close. They are the ONLY thi ng providing the split supply. I am thoroughly underwhelmed by the design o f that thing.
Of course I am spoilt. I had a Tektronix scope by the time I was 13. I've h ad a Wavetek generator for over twenty years I just had to throw in a filte r, but it is fine. You should see how THEY make a sine wave. That impressd me somewhat. They use a three stage slope modifier to a precision triangle wave which is totally frequency independent. There is no AGC nor is any nee ded.
Anyway, all you need is a couple of Zeners and probably some 22 uF caps to go across them. If you want batteries, there are plenty of ways to charge t hem. Plus they are bound to be smaller and lighter.
Bottom line, it is probably working correctly when plugged in. It probably has more harmonic distortion when not, but that is not for sure because it is a Wein bridge oscillator. It may be very little and you need a distortio n analyser to tell. It takes quite a bit of distortion before you cna reall y se it on the scope.
I was reading an article about that. If you can print the scope trace and h ave datum points, you can use a ruler to determine how good a sine wave is. I didn't read the whole thing but it was kinda interesting. Maybe I'll get back into it. If you want it I'll Dropbox it.
Anyway, two Zeners and two lytics. for now.