> Bias voltage is derived through the voltage drop across the grid resistor which is discharging the input capacitor.
Yes, at "high" signal levels, the cap and grid-diode rectify the signal peak and create enough bias to stay out of sustained clipping, though gain goes down.
At no-signal and small-signal, there is another effect. It is not well documented, but was widely used. We assume that grid current is zero, or small-but-unknown; this is not really true. For reasonable plate voltage and cathode curent, some cathode-plate electrons accidentally strike the grid. If you put a resistor grid to cathode, the grid goes negative. If you observe the spec-sheet rating, typically 1 Meg Max, this voltage is negligible. If you wildly exceed it, with 10Meg or 20Meg, you get several tenths of a volt negative grid bias. If your source is AC-coupled and does not exceed a few tenths of a volt, amplification is high and linear. For best results, use a hi-Mu tube and a large plate resistor; this tends to stabilize plate current (and by implication, plate voltage and grid voltage and max signal level).
A particular advantage is no cathode cap, which was problematic when electrolytics were leaky and short-lived. You do generally need a film grid cap, and it must be much bigger than you'd think for 22Meg, but it can be as low a voltage as you can buy.
Fisher and others did this as the 2nd stage of a NFB phono preamp. Signal level there (inside the NFB loop) is 20mV-40mV tops, and this avoids the LF zero of a cathode cap and a bit of bulk in a tight layout.
Many PA amps did it this way because in normal PA amp use (before Rock and before wide use of hot Condensers) the mike levels never got near a tenth volt.
It was common on early guitar amps because early-1950s pickups and playing styles didn't exceed a few tenths of a volt peak, and this trick does tend to give the ab-max gain the tube is capable of.
I think it fell out of favor in late-1950s guitar amps because hotter pickups and harder playing styles gave levels higher than grid-leak can handle. Alnico, hum-bucker, the transition from brass/sax bands to guitar bands.
It stayed in favor in the CHEAP models, like KAY, and in many home phonographs, right to the end of tubes.
> plates are at pretty low voltages (18 and 62 volts)
That does not sound right. Assuming there is +250V in the box, you expect plates to sit above 50V. Check for leaky grid/plate coupling and B+ de-coupling caps. Replace the tube. Check for drifted resistors.