I bet that got some peoples attention! Let me lay it out first.
Removing and replacing bathroom exhaust fan in 20s house. Old fan was put in x number of years ago (80s maybe) using ROMEX® and a wall switch that tapped into the bathroom light circuit for power. Bathroom light had to be on for fan to operate. Not ideal. Also no outlet.
So new 20A circuit from panel will go in to feed GFCI (load to timer switch for fan). Easy enough.
However removing old ROMEX® wiring left a 1/2 inch length of the old rubber and cloth insulated ceiling wiring bare (no box, just a mid-air splice). It had been stripped, twisted, soldered and taped but popped off during removal.
All the rest of the old knob and tube appears clean and pliable, and this wire will only feed the light fixture running 2 cfl bulbs.
The question: Can I use a bit of rubber insulation (from a piece of k&t in the scrap bin) the length of the gap and tape it up with Super 33? It isn't a splice anymore and it would be serious project creep to try to follow the wire back to the switch and replace (at least two knobs, several tubes and 15 ft of unknown). If it hadn't popped off would it have been proper to cut back the spliced ROMEX® and then cap and tape it up?