I replaced a toggle (off/on) single switch that controls both the vanity lights and a ceiling light in my bathroom. However, only the ceiling light turns on. Is it possible while attaching the wires to the new switch, the wire to the vanity fixture came off? Could there be another explanation?

Just moved house and have a problem with exchanging all 12V 35W halogen bulbs, with 12V 5W LED bulbs. The latter work well for about 5 minutes, then start to (very weakly) flutter. After another 5-10 minurtes, some of the bulbs turn off. When I switch off, and then on again, the bulbs light up - again for another 5-10 minutes, and then the problem repeats itself. I note on the transformers concerned (see attachment), the phrase 'for 20-105 watts'. This is achieved with 2 halogens (70W total), but not for 2 LED bulbs (10W total). Is this the problem? Why should too LOW wattage give problems with the trafo?