So... how do you test tubes, other than to follow the signal through the circuit? Just curious. I have no intent to mess around with tubes.
The tube folks had large test benches for that. When I toured Richardson Electronics somewhere around 1988 or so, they still had several, and the pieces of a transfer line to build an industrial welding tube.
You need to be able to measure and vary bias, plate voltage, screen voltage, etc. That's how those curves of gain etc are generated.
To match tubes, you would likely set a bias voltage, and group the tubes based on their plate current with some specific plate voltage and screen voltage. Your choice of bias voltage is based on the tube characteristics, and the "spread" you get.
Alternately, and possibly better, you could set plate voltage etc, and measure the grid bias needed to get a specific plate current. That would give the best indication for a specific amp, like an SVT, where the desired idle plate current is known, and bias voltage is adjustable.
For a fixed bias, like the Mesa, you would use the fixed bias voltage, and select an acceptable grouping around your target idle plate current.
To match gains, you'd do different things.
The standard tube tester cannot do any of those measurements in a meaningful way, although you can, with some, get a VERY rough matching. You need to know details of the tester circuit to know if that is possible or not.