OK since it is impossible to get the lamphouse plug and socket reversed, let's begin with the other connections. The power supply 120 volt cord and plug need to be plugged into a constant supply (read wall outlet).
At that point with the power supply switch off, you should have no voltage to either the 120 volt outlet on the rear of the power supply, the timer cord and plug, or the cord to the lamp house...as indicated by the lamp not lighting.
Next with the power supply cord to the power supply plugged into a wall outlet turn on the power supply...you should have no power to the enlarger lamp. However you should have 120 volts nominal to the 120 volt timer plug on the rear of the power supply. You also should have 82 VAC to the timer cord plug. This the one that probably shocked you since it is a male plug with exposed terminals.
When you plug the timer power supply into the rear of the power supply and the power supply plugged in and the power supply turned on you should have an indication that the timer is energized...but you will not have any power to the enlarger lamp or fan.
Next with the timer plugged into the 120VAC socket at the rear of the power supply, the power supply plugged in and the power supply turned on you should next plug the timer plug from the power supply into the enlarger socket on your timer and your enlarger should now power up for focusing...turn off when the timer is turned off...turn off when the power supply is turned off and you should have the timer controlling the exposure when you call for the timed function on the timer.
These enlargers operate with 82 volts to the enlarger lamp...therefore the 82 volt power must originate from the power supply (step down transformer) feed through the timer relay and then back to the enlarger lamp. The 120 volt is there simply to supply voltage to the step down transformer in the power supply and to supply the control voltage for the timer that you use. I would seriously doubt, barring someone playing electrician before you got it, that you have a problem...the only problem that I could see is a stripped wire going to chassis ground (would trip the control fuse on the rear of the power supply) or a relay with frozen contacts (unlikely since you have tried a number of different timers.
I seriously doubt that you have a ground problem since the ground circuit is only involved in the event of a voltage leak to chassis ground. It is a safety on the unit. The ground is not involved with either of the two voltages involved or any of the control functions. This is AC and not DC voltage.
Hope that this helps.
Best regards,
Don
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