Our kitchen has some halogen downlighters under the cabinets, and a little
sensor which causes a relay on top of the cabinets to click when you wave
your hand underneath. There appear to be *no* switches anywhere for this
stuff, and the lights don't come on. How are these things usually wired up?

Hi
Many possibilities abound but here are a few'
1 sensor is a separately powered piece of kit in its own box usually dumped
on top of the cabinets ,this has a relay (which you hear clicking) which
switches the downlights on.
2 You have a 'sensorlight ' system. A custom unit which contains everything
including the downlight feeds.
3 You have a sensor and power supply which then drives a separate relay unit
which again controls the downlights.

Best bet is to investigate the wall unit tops for metal boxes (or if the job
has been done correctly) a control unit mounted in a cupboard or on the wall
above the units.

Look for a switched fused spur (similar to an immersion heater type switch)
connected to the unit.

Any metal boxes should be marked and may have a low voltage fuse for the
downlights that has blown.

Or as (unfortunately) in most cases all the downlights are chocblocked to a
free standing transformer ,look for a loose wire.

It goes without saying turn of the mains before checking any wiring.

HTH
CJ