Circuit testers come in many types mine has a series of leds first two for 6 volt and also show + - or AC then 12, 25, 50, 100, 200, 300, 400 volt and with your transformer I would expect 3 leds i.e. up to and including 12 volt on output side and up to and including 200 on input side. But my other tester only has 4 neons 50, 100, 200, 300 volt and this would not light at all on the output side. So sorry the info on tester use tell me very little. I would assume you tried putting the original lamps back? And also switching off allowing to cool and switching on again?
A small amount of moisture is unlikely to be a problem so soon but will in long run. But current is high around 16 amp so any bad connections will soon cause a problem.
And are you sure originals were Dichroic with the low voltage types the bayonet connection will not allow the Dichroic to be fitted into a non Dichroic holder but with extra low voltage there is no protection against fitting wrong type and Dichroic are designed to allow heat through the reflector but reflect light so behind the light gets very hot but the standard mini spot light reflects both heat and light so behind the lamp runs a lot cooler.
Note:- Low voltage is 50 to 1000 volt up to 50 is called Extra low voltage.
Also wattage is also a problem where same physical size bulb can be 10W to 75W and I have seen them get mixed up before and burn out transformer.
Garden lamps are often very low wattage.
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