Loops of open-reel tape. Kids today wouldn't believe it.
My theatre tech days coincided with the rise of second-generation MiniDisc, which provided seamless looping and rendered such tactics obsolete overnight. Strategically placed hooks and nails for looping tape were still a common feature in sound booths, and competently splicing 1/4" tape was one of the items on the training I did to be approved to use the kit in Brizzle Students' Union. Never used tape on a production, tho, unless you count recording to DAT.
These days it's all computers, of course.