Silly question, but are your GI leds correct "AC leds" and not "DC leds"???
....meaning, the 'AC" ones have an internally fitted diode-rectifier to ensure AC becomes correctly polarised DC on the Led?? if DC leds are put in the AC installation, they'll cook and overdraw current.
( excuse my ignorance, as i haven't used Leds on pinnies myself, and perhaps ALL pinny leds are "AC ready"??? ).

Maybe pull all the GI leds out and re-measure the AC volts, does it rise from 7.2 upto 8 or 12 or something?
Perhaps place 1 led-at-a-time back in the GI, while monitoring the multimeter for an obvious drop caused by a dodgy led????

my 20c ;-)
MM.
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Ahhhhhh yeah, didn't know there were different types and all bought from pinney suppliers. I can do the checks but this problem has been around (I reckon) from purchase when only candies used. This may be misleading but I did notice soon after purchasing that one globe was missing from the backbox. Being finicky I had to put a globe in. I think after that the connector cooked not long after and the first header/connector fixit occurred. When the GI's go, it tends to be in the back box.