Most component testers require removal of a component to test it. [Mr Carlson] recently restored an old Paco C-25 in-circuit capacitor tester. He does a very complete video tearing it down and showing how it works and why.
The tester uses an eye tube (sometimes called a magic eye tube) as an indicator. A 40 MHz oscillator produces a signal that finds open and shorted capacitors. You can also measure resistance, although you have to wonder how accurate it would be in circuit. If you want to read the original manual, there are a few copies online.
Examination of the schematic shows that the device doesn’t have a standard DC power supply. Instead, it uses self-rectification of the tubes to convert line current to rippling DC.
[Mr Carlson] has good advice about restoring these old boxes and some general advice about working with old gear in general. Honestly, we wouldn’t recommend using a device like this for practical use today. However, if you are interested in restoring old gear, this would be a good first project. These are available at relatively low expense. There are not many parts and it should be pretty easy to get one in working condition.