Isolation transformers are a very important part of any CRT repairperson's toolbox. In general it is an important safety tool because, in the event of you touching a hot chassis CRT, it isolates your body from being a conductor between AC voltage in the TV and earth ground below your feet, but it can also protect your equipment such as oscilloscopes which are not battery powered. Any equipment connected to earth ground can carry that ground into the TV and defeat any isolation, so you must have your oscilloscope plugged into the same isolation transformer as the TV, or a separate isolation transformer.
For some reason, a lot of the isolation transformers sold on Amazon still have earth ground connected internally. This completely defeats the safety purposes for CRT repair, so they need to be modified. The modification steps vary by model, but your goal is to disconnect earth ground from the isolation transformer. This is generally as simple as cutting the ground pin off the power cord, but if you want to make the change reversible you should open up the isolation transformer and find the earth connection inside and physically unscrew or desolder it.
I personally use this Tripp-Lite isolation transformer - you can do ground isolation by taking it apart and removing several spots where earth wires are connected inside. If that transformer is unavailable, you should try to find one with equal or higher wattage and an equal or higher number of plugs on the front. It is very helpful to have two plugs on the unit, one for quick use and one to plug an extension cord into for more plugs. Or, one for the TV and one for your oscilloscope - etc.
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