That's exactly what we do. Isolate the Air Data by disconnecting (the fittings are self-sealing when removed).
We then apply pressure into the static system. This can be done either with the test box or low pressure regulator.
Then..... we use leak detector to spray down the lines and fittings. We'll have bubbles at the leak point.
I've tried the acoustic tester, but we have better luck with the liquid detector solution.
I've run pressure up to 8 PSI for most leak searches. Higher pressure can be used, but 8 seems to work well.
Most of our leaks are fittings, either elbow or "T". They get hairline cracks in the threads. We see this more in the winter when the aircraft are left unpowered in the winter and everything inside freezes.
Backing up to the Pitot/Static line isolation..... a schematic of the system should be consulted before starting the whole process. Every item (especially analog instruments that still use internal bellows) has to be isolated as you stated above. A full set of caps and plugs of different sizes in a box helps.