It would depend on how the 10x2min were executed.
If doing them with a 30sec rest interval (RI) , for example, they would draw more and more from the aerobic system. If the RI was longer it would allow more recovery and more of the anaerobic contributions. Not useful for your particular circumstance described.
For a particular event anything more than ~1min, and definitely longer than 4mins will be determined by aerobic power. Hence all the things that go to building FTP will be the main focus. Main three ways to do this, push up the FTP, pull up the FTP or the sweet spot. All three can work, and to a point all three should be used.
Push - the traditional concept of base then building on that and then a bit of speed/taper etc.
Pull - the reverse periodisation model - shorter harder stuff, raise FTP, then go long (good for those in cold climates!)
Sweet Spot - just hitting volume in the sweet spot range to drive FTP (wattage groups love this one).
There are lots of other theories and methods that are used, and sometimes used well.
The key thing to remember are the three key parts of ANY training - stimulus -> recovery -> adaptation. You need all three. Otherwise you're wasting your time. In a lot of riders I often see the first part done well. The next two... not so much. Some rest well, but under-eat, so the adaptation doesn't take place, they don't *recover*. And if you don't recover, and you introduce more stimuli you just start to go down, down, down.
...actually I don't think you asked about any of that, but I like to rant about these things.
As you mentioned pacing is also crucial. Starting too hard will kill any TT, especially those of the uphill variety as there is no respite, no coasting and wind is less of a factor, hence as soon as the power drops, the speed drops. HR is unreliable in this manner to start so speed will have to be a proxy for power when you are practicing. The start should feel easy. Then settle into a goal pace for the interval/climb and then
hold on for dear life.