The purpose of any punishment is to provide a corrective learning experience. In light of that understanding, what do you believe you are teaching your 12 year old with the "Time out" technique? What do you believe his take away from that is?
There's a lot more unsaid but alluded to in your description: Him "Always being difficult", and going from Private school to PS...and how he handled all that. You guys have had long term problems, which might require a more professional approach...are you all in therapy?
The short answer to your question is that "Time out" is basically psychobabble for removing a child (usually a very young one) from a situation that is over stimulating to them so they (and you!) can regain composure. For older kids...over, say, 9..and certainly by 12....I wouldn't refer to it as a "Time out" as it is initializing, condescending, humiliating, and antagonistic...even though the actual suggestion is a good one. Rather, I'd suggest they "Take some time" and think things over, or I'd suggest they "Chill in their room", etc. Semantics matter.
To be effective,any punishment needs to provide a corrective learning experience. For that to happen, the parents response needs to be targeted to the behavior as well as the developmental issues of the child. If your son doesn't respond to the "Time out" suggestion, try modifying it just a bit so it doesn't sound so humiliating to an almost teen...and if it still doesn't work, really consider getting some professional help here...before he becomes and actual teenager and the issues (and his responses) increase in an order of magnitude that will really make things intolerable.