The 5th gear lamp operating switch is incorporated as a second contact within the neutral switch - the black bakelite block held on by three 5mm screws above the engine sprocket. I cant see how that could suddenly start lighting in 3rd or 4th gear, unless possibly the internal brass contact has come adrift or become bent. Might be worth taking the neatral switch off and checking there's nothing conme adrift.Don't overtighten the screws when refitting the switch, though - it's all to easy to crack the bakelite cover.
The other thought is, it's not simply a short in the wiring loom that happens to co-incide with use of 4th gear, is it? All the Neutral/5th gear switch does is connectr the relevant wire to ground to light the lamp.