I had 2 sets of Schwalbe tires with the loose 1cm of reflective tape. I've been riding on them for 4 years without them coming free. That loose bit is just where they join the two ends. You might be fine just doing nothing. A tiny dab of super glue would likely be fine too.
Yes they are they are the ends your right. Yes i think it would take a while to come free. I just thought i would neaten things up more than anything. The lectricians tape thats on it comes free and i keep replacing it :0)
Well got it today and seems to bond quick. Glad i wore gloves. Bit of a smell when i got too close to it with my nose otherwise easier to deal with than most glues. Thanks everyone for your help and will post again if it doesnt stand the test of time