Yes.  You need to get hold of a multimeter and check out what voltages
are available at the bulb holders with the ignition turned on and
reverse gear engaged.

I'm not familiar with your particular model, but I would expect that the
outer contact of the bulb holders should be connected to chassis (check
with meter set to measure resistance [should read 0 ohms]). The centre
contacts should be fed with +12V, from a switch mounted on the
gearbox/gear linkage.

If the resistance between holder and chassis is greater than a couple of
ohms, you need to sort that out.  If 12V isn't present on the centre
contact, then you'll need to locate the switch on the gearbox and ensure
that it is correctly located, that there is a 12V feed to it, and that
the the 12V reaches the other switch contact when reverse gear is
selected.

The results of these tests should narrow down the areas for further
investigation.

Just a thought - I know that some Audis have the reversing lights
mounted on the boot lid, and a common point of failure is the wiring
between the main body and the boot lid.