I can't speak to the collecting value of taped boxes one way or another but from an archival point of view, I can see two safe options. One is to use acid free "scotch" tape. Most stores commonly sell this now because of its safe use for photo albums (remember those from pre-phone camera days? :-). It shouldn't crack or yellow.
The second option would be to use archival mending tape, which you can find in art stores. It is much weaker and more like rice paper but if you just want to shore up a tear and keep a flapping flap from flapping and tearing off even further, it might work. Your mileage may vary with this one, and I suggest you use it on the underside of the tear because it tends to be opaque.
Tomlinson Run Railroad