My 412Hot Rod Deville has terrible humming/white noise when distortion channel is on

On mine, the guitar input jacks get tarnished and causes all kind of interference and noise. Take a Q-Tip soaked with WD-40, run in down into the jack and brush up and down. Don't overlook the filter caps as they are a common cause of noise. You need a capacitor checker (the older tube type) to thourghly check those out.

Are all the tubes lighting up? they should glow like dim light bulbs. If not, replace them with the same model type (12ax7, or EL34 for example).

Often there are two fuses, one to protect the speaker and another to protect everything, it sounds like the latter fuse may be burned out. take it out and take it to radio Shack for exact replacement.

This is because your clean channel only runs through the pre-amp section, requiring an increased volume level to match that of the volume of the drive section which is overdriven by the pre-amp circuit. my suggestion is to use lower volume level on the clean channel of the amp. To get any volume boost you may need to match the two channels you could use a signal/volume booster or overdrive pedal between your guitar and amp input, switching it off and back on when you switch back and forth between channels.

Hi. If the volume and drive levels are considerably low but you still hear a noise, you may want to consider trying a different guitar cable. The noise may be coming from a ground loop which is being amplified and overdriven by the amp itseld. I hope this helps. :-)

Realize that the number on the volume control is only relative... it means nothing regarding what the amp can produce. With a high level output guitar you can easily drive the amp into distortion at very low volume control level settings... what counts is the actual output sound volume and specifically the voltage output going to the speaker. Once the amp reaches saturation, any further input just pushes it into distortion or "flat topping".
An oscilloscope on the output will quickly show when amp starts to flat top.

There are many components in the system. Electrolytic capacitors are most suspect. C49, C50, C45, C51

There are many others but these are top suspects. You MAY be able to detect a change by cooling these components with circuit cooler spray.

ALSO check the +/- 16 volt power sources in the unit.

I suspect the power supply has an issue. Most likely bad filter capacitors. This could cause "motorboating" where power is drawn and supply voltage collapses and then recovers repeatedly.

Time for the repair shop. The parts cost should be nominal... labor... well...

It could be a number of things. If your amp is plugged into the same circuit as the lighting system it is the usual source of hum. Whatever you do, do not remove the ground prong from your plug on your power cord. Check at a music store and ask for a hum isolator. They make really good ones now that are not that expensive.

It sounds like a filter capacitor(s) has failed. The electrolytic caps dry out and cease to perform allowing unfiltered power to reach the preamp sections and get amplified.

Being this is tube with high voltages, an experienced person should work on it due to shock danger.

I assume you checked the tubes for shorts as well as emission since a heater to cathode short could cause this as well.

If the footswitch is not switching correctly, open it up and check for any shorts or a defective switch. Sounds like it's a problem with the switch.