Bicycle Tutor

I have changed the handlebars on my son's bike for him and repositioned the gear change from the post to the bars. Now the gear shift lever, when in the lowest gears is changing all by itself into the higher gears. Whilst this automatic feature could be useful, it is not very practical for him! I have tried tightening the tightener but that didn't work. Any helpful suggestions very welcome, from sunny but chilly Oxford, U.K.

Do you mean that the thumb changer is moving on it's own and not staying where you put it?
You say you tightened up the "tightener" - is that the black "wing" nut on the top?
This is a friction device for holding the changer so I can only suggest stripping it and cleaning and checking it initially. If it's been apart has a washer or part dropped out?

The washers (friction cups) should be clean and NOT oiled. Undo the black wingnut all the way and the unit should come apart. Clean and re-assemble and tighten the wingnut until the friction is correct. Not to tight, just enough to hold the lever in it's set position.

Just wanted to add those handlebars look almost like my Armstrong ones (Raleigh). They're real nice.

Thank you. I will give it a go.
(Yes, the lever is moving by itself and the wing nut is perhaps slipping.)
Little son was not that comfortable with drop handlebars on the mini racing bike and letting go with one hand to change gears, so he now has some 'sit up and beg' ancient and heavy handlebars and gears nearer to hand. Seems fine, and meanwhile he is growing. Cheers.