Hello.
Personally I would turn the circuit off.
I would then cut the cable to each light in turn that doesn't work, in a place that you could crimp it back together.
Switch the circuit back on, (with the lights switched on)
Then measure the voltage present.
If its 12v, you can put the fault down to the fitting's ( these lights can 'break down' under the heat over the years) , replace and crimp.
If not, then you need to get to the transformer so taking down the necessary sections of ceiling is the only way I see of doing it.
As, due to no access, we dont know if the lights have thier own transformer per unit, or whether they are all connected to the same one etc. it's hard to say how much ceiling has to come down.
All joint boxes and screwed connections used to be deemed ok left in un accessible places, ( under the floorboards etc) but now it's a no no.!!
Hope that this is of some aid.