only gsrs and type Rs have vtec for integras, and they only come in manual. i drive an ls auto and you can hit the high rev ranges by just flooring it but you don't have the control of an manual
If it doesn't engage why would honda have put it on auto GSR's in japan, auto B16 civics and auto in their accords, and civics and most of their cars now days. Clarify your post it doesn't make sense.
Honda has them equipped in most of their vechiles now. auto or manual. So it must make some sense of its coming from the factory. Take Hp's advice and read. You will learn alot.
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