Hallicrafters S120 hum at no vol and hum with volume

[Electronic M]

When you say last and first tubes in the string that is rather vague...Better to refer to them by their functions: converter(AKA 1st detector), IF, Second detector/AVC/1st audio, audio output (at least that is what the line up would usually consist of in an average selenium powered AA4).

Do you have any clip leads (that have small alligator clips on both ends)? You can pull a tube (google it's data sheet to find the heater pins) and use 2 clip leads to reconnect only the heater leads to the circuit....It is simpler than using a light bulb. Avoid using the light bulb as a substitute heater the bulb has to have the same voltage drop and current rating as the factory heaters or it will not work (and it could burn out the other tube heaters).

Got a diode and a small cap .001uF or less? You can make an AM signal tracer easily just use the diode as a detector and the small cap to filter RF out of your listening device. You can even add an amp* between the detector and the listening device.

*Make sure the amp is battery powered or that there is a power line isolation transformer powering the radio.....If you neglect that then you could create false hum from connecting devices with different signal ground references, and or damage the devices.