You are mixing up your currents and voltages. The percentage is about voltages and not current. The current is equal through both the lamp and the DUT.
Take your example of 700W lamp and 500W DUT, assuming the DUT is a normal resistive device and for the sake of the argument that the lamp is too, will result in the lamp seeing 41% of the voltage, which means that it will glow at only 41% of the brightness. The DUT gets 59% of the voltage, which means that it will not go up to its full potential.
Lets say the DUT is a normal resistive heating element rated 500W at 240V. This means it has a resistance of ~115 Ohm. The lamp rated 700W at 240V has a resistance of ~82 Ohm. The total resistance of the series network is 197 Ohm. So the current through this series network is 240 / 197 = ~1.22A.
The voltage across the heater is 115 * 1.22 = ~140V, the voltage across the lamp is 82 * 1.22 = ~100. This shows that the back of the envelope calculation is correct. 100 / 240 = ~41%
But the power consumed is only 240 * 1.22 = ~293W, which is no way near the 1200W sum of the device wattage's. The heater is only generating 140 * 1.22 = ~171W of heat.
As I wrote earlier the real world of lamps is a bit different due to the fact that it has a positive temperature coefficient, which means that the resistance goes up as the temperature rises. So initially the 700W lamp will have a lower resistance and will only be around that calculated 82 Ohm when fully heated. This changes the above scenario and the heater will get a larger slice of the voltage, but one needs the resistance vs temperature vs current curve of the lamp to determine the actual value.
You should evaluate the need for and what wattage to use on a per case basis. A transistor radio requires a different approach then for instance a cathode ray tube television. In a more modern light, a lot of devices make use of a switching power supply that is separate from the actual device itself. This allows for working on the device at a lower voltage by using a current limited bench power supply. This way the current limiting
lamp indicator on the supply can take on the function of the lamp.
If the problem is with the switching power supply it becomes a different story for which the lamp can be of use.
As I'm not a real repair man, I don't have a dim bulb tester device, and tend to stay clear of the mains voltage. Have had enough shocks throughout my life.

One anecdote, I once worked on a simple transformer based linear power supply that had an issue. I constantly removed the power cord to make some changes, right up to when it was working again and needed to be put back together. I never knew I could jump that high.
