Hmm, really pick and go situation after 8 pm to 2 am? I
thought queue is always long at airport.
I used to like Terminal 2, but I had a bad experience last week,
think is on Monday. I reached T2 slightly before midnight, T1
queue was very long, stretching to the junction to T3, so I go to
T2. I think it shows that there are 3 flights arriving at T2
(cannot really remember). The queue was slow, and after
queuing for 1 plus hour, it practically stop moving. I
started to see taxi started to leave the queue and the queue move
is practically based on TD leaving queue, not base on TD getting
pax. Till about 2 am, I was not far from the queue, but it
really not moving, then finally someone told me that there is no
more flights. I go inside the airport to look at the flight
information and indeed, next arriving flight is at 6 am at
T2! So, I finally decided to leave airport.
I had the impression there is always arriving flights every hour
but that experience prove me wrong! Now I roughly browse
through the arrival flight details from
(http://www.changiairport.com/flight-info/flight-status/passenger-arrivals)
before leaving home. Good luck all!
Maybe you should try T3 after midnite.
Esp the SQ15 arrival from Seoul ICN | San Francisco SFO.
Ho sey ah, that one very few connecting pax. Almost 270 pax one
flight come out, but at 1a.m plus. Tried and tested. This flight
usually delay a bit out of ICN. Almost always pull into T3, only
once out of like 30 times in T2. I frequent flier on this
particular route, that is why I know that. 
SQ11 arrival from Tokyo Narita NRT | Los Angeles LAX another
super one. They use the 744, but this one a bit more connecting
pax, especially the Jiponese ones who connect at T3 for the
earliest morning flight out to SYD, MEL and PER. But on the whole
still ripe for picking.