I think you have to ask yourself the question 'when do I want the new lights to come on?'
If you want them to be on all of the time, pick a positive (any positive) that comes on when you turn on the ignition. If, on the other hand, you want them to be on with high beam only, then you need to find the positive that feeds the existing high beam and connect to that.
The short answer is that both these positives will be connected to the headlight bulb via a plastic connector/plug, so get in there and take your pick. You won't know which one is which until you try, and you'll have to test to confirm once 'connected'.
The longer answer. I'm making one big assumption here, and that is the fact that being 'LED' lights, the current draw is going to be minimal, and if that is indeed the case, then finding your 'switched' feed as mentioned above will be fine. If, however, these new lights will be drawing any 'substantial' current, then you should be feeding them direct from the battery and using the 'switched' wire to 'turn them on' via a relay. What is substantial current? I don't know, I'd guess at anything approaching 250mA, anything more will, 'perhaps', start blowing fuses.
Anyway... once you've found your positive, you can indeed 'splice into it' as you've suggested. Best and simplest way is via one of those little blue connector things that just crimp on without having to peel back insulation and all that that entails. Don't forget that you'll also need a negative feed, found anywhere for your convenience.
Best of luck.