IIRC that is a simple emission tester with no active components inside to need warmup. Replacing any paper or electrolytic caps is a good idea, however.
As far as testing, check a selection of known good and known bad tubes and see what results you get. Emission testers aren't the best way to test a tube, but they are a bit better than nothing. If there are internal adjustments, you will need the manual to figure out how to adjust/calibrate the device.
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