Yes, "end-of-reel tape clips" is what the things in Scotch (3M)
reel-to-reel tapes were called. The 1960s. They came gratis in every box of Scotch
recording tape. When new, the tape-ends were held down by a slender piece of
tartan-patterned pressure-sensitive tape on the edge of the reel. One
sliced it off and was ready to use the tape.
The tape clips were small, about 1/2" vertically in length on two sides,
rounded on the bottoms, and just wide enough to fit over the tape and
inside the reel, with a slot at the top. One was supposed to squeeze the clip
sufficiently to permit the end of the tape to be caught in it, then slip the
ends of the clip down over the tape on the reel. There were other such
devices and I might have a few here, but since I always bought Scotch recording
tape that's what I mostly had and have.
I never used them and still do not. Sorry to go into such detail for
ARSC members who already know all of this. More in replies to other messages.
I think I found what you seek. On the inside of the box of some
early Scotch tapes: No. 12 - End-Of-Reel Tape Clips.
"Clip securely to tape, prevent spilling or tangling in handling,
storage and mailing. Fit inside reel, won't distort reels in
storage. Work equally well on partial or full reels."
Hope this helps.