For Nest Thermostat 3, I am trying to identify a common wire on my old HVAC. The diagram can be found on the link below:
Whenever a furnace has a 24V low voltage transformer, the two 24V terminals are R and C.
If you can't find any other way to do it, pick one of these two low-voltage terminals to use for C.
Worst case, you picked R by mistake, and the thermostat will see 0 volts between R and C, since you are actually bringing it R and R. In that case, use the other transformer terminal.
On your furnace, the low voltage transformer is in the smaller schematic to the middle left. Within that drawing, it shows the transformer in the middle. The R wire snakes through a limit switch to the thermostat connection terminal block on the lower left. Your furnace does not bring C out to that terminal block. You'll have to "go get it".
Grab a piece of (blue) 14AWG THHN with a piggyback crimp on one end, and run it up to the top left terminal on the transformer
It appears that the C wire from the transformer runs off to the control board on your system, then gets lost in a way I can't trace in your photos However, we know it is available at the top left terminal on the transformer as that terminal is jumpered to the chassis (visible in your photo of the upper compartment), so we can turn the unit off at the breaker, take a piece of (preferably blue) 14AWG multi-rated wire (THHN/THWN/MTW/AWM), crimp a piggyback crimp terminal to one end, remove the existing yellow and white wires from the top left terminal on the transformer, slip it on the piggyback crimp, slip the piggyback crimp back on the top left transformer terminal, then stuff the new blue wire down through to the lower compartment and nut its other end to the wire you want to use for C, and turn the power back on at the breaker.