Mounting potentiometer, horizontal, 470 - 500 k ohms, linear. The raster of the pins (spacing of the pins / holes in the PCB) is important. It will probably be 5x10 mm. For example: c
Don't touch that potentiometer, it's good. You have a problem with the transistor, you probably did not install it. The reverse soldered transistor should not break down, because it works at 5V, which is lower than the base-emitter zener voltage.
This transistor is designed to amplify the fi1 signal, and feed it to the voltage doubler on C40, CR1, CR2 and C41. The voltage increased in this way, after smoothing in the R42 C42 filter, is given to the potentiometer, which sets the correct voltage on the GTIA pin17.
If the voltage on this pin changes from 0 to 7 ~ 9V while rotating the slider, that's OK. If not - check the transistor. What is the transistor model?
If you are talking about Q6 it is 3409, the same as it was on the board originally. As I wrote before, I put in this item a total of two items 3409, once the other way around, and then another item correctly. The voltage changes from 0 to 9V on the potentiometer as it turns.
The oscilloscope, as I understand it, you don't have, because you would have used it already. But if you have a multimeter, you can at least check the circuit statically. Before that, turn off the color (POKE 710,0: POKE709,0) because it will distort the measurement. The voltages should be similar to those shown in Jere's diagram.