when driving it on boost in second, and changing up when it hit the red line, you had a reasonable while before boost really appeared in third, and again from third to fourth.
Something's not quite right with it, if that's the case. If you are changing up at 6000 rpm in second you are straight into third at 4000 rpm and should have boost straight away. Out of third at 6000 rpm, you are taking fourth at 4500 rpm and there should be no lag at all.
It probably just has some little leaks in the pipework here and there.