Indeed look out the window. Watch your aiming point, and keep it stationary in the windshield. The old "non-moving point" technique of aiming a visual final approach. Subconsciously you will also be maintaining your pitch relationship with the horizon as well, and scanning airspeed and vertical rate. This will keep you squared into the glide path. PAPI and electronic GS etc will back you up.
I was in full agreement until the last sentence. I think the last sentence is where many (beginners especially) go wrong. Because they try to get everything to "fit". And below DA/DH or even several 100 feet prior, they won't match up (not co-located, PAPI calibrated for different eye height etc). Hence, with each scan, a new (inappropriate) correction is made:
"Glide fits?", "Crap now we have 3 red!" - *correction*, "ups now 1/2 a dot above the glide" *correcting again*.
^ A lot of unnecessary instability introduced into the path in the very last few feet, and focus on the instruments, at a time where the pilot should only concentrate on the aim point and speed.
Usually it lead to a "panic pull", when being surprised at seeing the runway come rushing towards the pilot who is now more inside, than outside - manifesting as a small break in 100-50 feet. Now a long landing at the end of the touchdown zone is inevitable... or passing the threshold in 75-100 feet, the pilot now becomes aware and delays the flare. To avoid a smack, leaves the throttles in until 10 feet -> airplane keeps flying and floats to the end of the touchdown zone.
It's so easy to see what is going on when you are aware of it. And usually, the after landing question "where did you look?", confirms exactly the above scenario.
Hence, my mantra "aim point, airspeed - aim point, airspeed" ONLY - from the last 300 feet LATEST or better 500+, phasing out the electronics aids slowly, the higher you switch reference to the aim point (visual conditions permitting of course). If the glide and PAPIs don't fit OK doing this technique, the chance is the approach was messed up before switching reference anyway.
Hence, in short: forget about the PAPI and glide as you are approaching the runway. They are there to lead you to the visual segment, not to lead you into the flare.