FWIW, the oscillator is a Wien Bridge, notorious from Terman and two guys H and P in a garage in Palo Alto.
Terman's idea, implemented by his students, was to stabilize the oscillator with an incandescent lamp NFB gain network. They got a patent, started a company, sold a few, designed a very cool case, got lucky, the company took off.
If you can tolerate some waveform distortion, you can hand-trim a Wien just past the start of oscillation. Amplitude rises until the wave flattens top or bottom enough to "lose gain". When I have hand-trimmed prototype Wiens, this is VERY fussy. The lamp-NFB makes it a little less fussy and more likely to work for years.
The other interesting bit: V2 of the Wien's amplifier is worked as a Cathodyne, two outputs. I have never seen that. If V1 has enough gain, no reason it can't work. In fact there is a near-Wien (a patent dodger) which uses a cathode follower (or WCF) at V2.
The two outputs do something to a pentode, which does not seem to be "in" the audio path, but closely coupled. My eyes are crossing trying to follow the lines. There is a "clever" 2-pentode cross-couple which varies audio gain without large variation of total DC current (thump). {EDIT} No, this is just a differential amp, signal in one side, silence to the other side, and out-of-phase LFO to the two grids. The signal side goes in and out of conduction, but the sum current stays near-constant.
The three inputs have nothing to do with it. Maybe they thought the whole band would plug into the one tremolo.