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.
