It is very unlikely this was ever done on legacy reel-to-reel tape machines, since the time to wind through a 2,400 foot tape to find the next block of data would have been ridiculously slow.
In commercial computing applications, the standard way to process a large dataset in "random order" was to start by sorting it into the required order. This could be done using sequential reading and writing with several tape drives. For example with three tape drives, you could first copy (unsorted) sections of the data onto several tapes, and then read a block of data from two tape drives, sort it in memory, and write it in sorted order onto a third drive. Repeating that "merge sorting" procedure enough times would sort an arbitrarily long data set.
In principle, the IBM S/360 tape drives could have done this, because they were capable of backspacing over a data block, and then reading or writing with the tape moving forwards. But writing new data in this way could cause problems, since the data blocks on tape could be of variable length, and obviously you could not replace a block by a longer one.
This "backwards reading" was used in some specialized applications - for example in solving systems of equations which were much larger than the available main memory, it was possible to write intermediate results onto a tape, and then read them backwards, while doing more calculations, and writing the final results to a second tape. I used software that worked like that in the 1970s.
There were various special-purpose storage devices that used many short loops of tape to achieve a reasonable random access speed, with much more storage capacity than the available magnetic disks (which often had a capacity of only a few Mb, not a few Tb as now) Once such device was the https://en.wikipedia.org/wiki/IBM_2321_Data_Cell.
Hardware failures on the 2321 and similar mechanical devices could be "entertaining" - the data could literally end up being shredded and scattered around the computer room floor!
Later, the https://en.wikipedia.org/wiki/IBM_3850 was a much larger scale version of the 2321, using tape cartridges storing about 50Mb with a robot device to mount the tapes onto drives and transfer the data to disk for access by the computer. By 1980, the largest model could store about 500Gb - but in a 20-foot-long cabinet, not a 2 inch diameter PC disk drive!