Finding the c-terminal on my furnace
From looking at your pictures I have extracted what appears to be the key parts. Please verify for yourself but it appears that the RED wire from the transformer goes off to the thermostat cable terminal block. If that is the case then the opposite terminal of the 24VAC transformer would be where the C wire would connect.



My suggestion for connecting to the transformer terminal, where there are presently a brown and a black wire connected, is to make sure the wires are terminated properly with spade terminals rather than trying to just twist a wire around under the screw.

If you wanted to make this a clean upgrade you would look at changing out the current terminal block with one that has three positions. This way the thermostat cable can just terminate at the terminal block and you can add an additional wire from the terminal block over to the transformer.



(Picture and Supplier Source: https://www.mouser.com/ProductDetail/Bussmann-Eaton/TB300-03?qs=sGAEpiMZZMsntO7gZZwOWCUaS%252b%252blAGE8Ob7nLJyRNq0%3d)