Perfect.
Check that there is a noticeable delay between when you turn the switch to on and when the light changes color. The same delay should exist when you apply music. The 1k should add a delay when you move the switch to on. That probably wasn't there before.
This still leads me to suspect Q2 based on the other measurements you did.
That said remove Q1 and Q2 and check the gain and compare against the datasheet, otherwise just replace Q2 and possibly Q3 since you don't have a way to measure leakage.
Actually have an idea: With the switch in the OFF position and no music, measure across R41. Probably millivolt scale.
Also do the same for R38. This would be an attempt to determine which transistor is leaky. The leakage current would be I=V/R providing the transistor is not turned on. Gains being different than the suffix value
2SA1015 pdf, 2SA1015 description, 2SA1015 datasheets, 2SA1015 view ::: ALLDATASHEET ::: would also be a clue.
So what I'm saying is that you may be able to determine which transistor is leaky by an in-circuit voltage measurement. Then by comparing the expected gains (use suffix and datasheet) with the measured gains to also tell. Finally, you can "give up" and just replace them both because you don't have a leakage tester or you can try to "create a leakage tester" with a batttery and a large resistor 10K-1M ohm through E and C, base open. Measure the voltage across the resistor to get a current. Should be probably 0.1 uA or lower.
Although the extra diode increases the delay, it does not change the fact that if it was left in auto mode and Q2 was leaky, there might not be a delay. Thus the 1K resistor makes the ON mode behave like the Auto mode in terms of delay. So, if Q2 were bad, there may be nearly no delay in auto mode but with the added resistor, it will exist in the ON mode which it didn't before.