You are free to abuse your own equipment, but you are better off all-around NOT forcing misfit sockets to fit. It's not an accident they don't fit. A lot of engineering goes into preventing them from fitting. Standards organizations hate defining yet another socket type, so they don't do it unless there's a safety or essential functionality reason for ...
You can turn the gas off to the furnace and then turn the heat on. The fan will go on but no gas so no heat. Not a solution if you want to run the fan often but I just needed to remove cigarette smoke from an apartment so I needed to circulate the air for several hours then done. Then have to relight the pilot.
The red cable that exits to the right of the picture is worrying as it seems to bypass the flue safety device.
According the the diagram C is blue wire between the gas valve and the transformer
so these are your "R" "W" and "C" connections
One of these two terminals on your control transformer is the C wire terminal. If you have a voltmeter, you can measure each terminal on the transformer against the R terminal. The C terminal will give you 24v, the other 0v (or close to zero). Of you don't have a voltmeter, you can simply use trial and error. You can't hurt the thermostat.
Tried connecting the C-wire (thin baby blue wire off the thermostat bundle) at the furnace end to a few different connections, but could not get the thermostat to turn on.
Of note, I was not putting the metal cover back on and finally realized the cover has to be on to compress a black switch in order for the unit to turn on. Success!
I'll include a ...
Ok, you'll need a voltmeter for this. Set your voltmeter to AC volts. Look on the right side of the photo. That's your control transformer. One terminal of that transformer is going to the control board to feed the R terminal. The C terminal is the opposing terminal on the transformer. Check each terminal on the transformer against the R terminal on the ...