Try pins 1 & 3 - it should be detected as diode with ~1.5V drop.
I read A ebook of CRT TV Repair ,It said that "when testing H.O.T, Most have in built internal diode between collector and emitter. Therefore if you measure between these legs you will get high and low."
So I think that It should get reading of some voltage and 0 voltage when I measure voltage between collector and emitter of H.O.T on diode mode.
I quote below guide from ebook of CRT TV Repair
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Little tip on how to test transistor
Tesing NPN transistor
testing between base and collector expect high and low on your meter on diode test.
testing between the base and emitter expect again high and low on your meter on diode test.
Testing collector and emitter expect high both ways.
Testing NPN transistor again use the same principle.
Use this rule when measuring the switching transistor(S.O.T) but when testing H.O.T please note that Most have in built internal diode between collector and emitter. Therefore if you measure between these legs you will get high and low.
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Test between C & E with the DMM in "diode" position. using the red DMM lead for C, & the black one for E on an NPN transistor.
Reverse the connections for a PNP transistor.
Initially, it will be an infinity reading, or something else weird, indicating a very high resistance.
Spit on your finger & use it to connect B & C.
If the transistor is functional it should turn on, giving you a reading.
If it has very little effect, don't give up, as power O/P transistors don't always have a lot of gain, & a "spitty" finger might be too high in resistance to bias the transistor, on so use a 4700 resistor instead of the finger.
If you use an analog multimeter, note that most of them have reversed polarity on the Ohms ranges, compared to a DMM.
Your transistor is almost certainly a 2SC 6090 , which definitely is an NPN transistor, used in the horizontal output stages of analog TVs.
Is it impossible to check HOT(C6090) with LCR-t4 meter?
Analog meter and DMM are quite different things when it comes to meter resistance of sonethig, that much more nonlinear than plain resistor. And transistor (especially high voltage) definitely not a simple resistor. So experience with analog meter could be not relevant to DMM one
I followed your instructions(set DMM to "diode" position. using the red DMM lead for C, & the black one for E. then put some water on one of my finger ,and placed it to pin of Base & Collector.)
And I found that It displayed 3.290-3.250V in DMM.