Yeah, that's them, exactly as you described. I think i probably mistook them for doves the first few times, but now i have realized they are actually reasonably common. And yes, in pretty big groups. However, they seem to be nocturnal, and at night their behaviour is quite different. fairly sure now that they're called savanna nightjars. There's an interesting story on them in the Taipei Times - apparently they were considered to be on the verge of extinction - now they're a safety hazard at airports. Also says their call can reach 90 decibells - people have started complaining, which is a bit rich in noisy old Taiwan:
http://www.taipeitimes.com/News/taiwan/archives/2010/01/18/2003463775

Here's a link to a video that includes their mating sound - you can check and see if you've heard it.
http://ibc.lynxeds.com/video/savanna-nightjar-caprimulgus-affinis/one-perched-rock-dry-...