Manu
Geoff gave you great advice.
eBay or CraigsList are good sources - Bunch of them on eBay now.
Welsh Ent (https://www.welshent.com/) has a pile of used parts - you may get lucky.
There is an outfit that provide panels covered in burled walnut:
https://www.etsy.com/uk/listing/724395335/jaguar-xke-e-type-wood-walnut-burl-dash – don’t know the exact site for them, though. they pop on eBay pretty often.
I’m gonna brag on myself and refer you to my thread. (I built it in the detail I did just for you (or – at least – someone who is starting out with a Series III)). Most of this forum discusses the Series I - II – which makes since since the 6-cylinder version accounts for ~80% of the manufacturing line. Mine is a 72 Series III OTS.
Lots of photos on it so you can scan the threads looking for images rather than trying to guess the text string I used.
In direct answer to your question, start with Part VI of my thread (I shift to a new “part” when a thread nears/gets close to 100 posts.) I am not a mechanic but I am happy/proud to say quite a few current/former Jaguar mechanics/restorers chime in regularly
Craig Restores a Series III OTS - Part VI - #5 by Craig_Balzer . Follow on parts cover more aspects, so search after Part VI.
I also have several videos on my YouTube that focus on the wiring behind the gauge and the fuses: https://www.youtube.com/channel/UCXJTFHII0M9ORwt5kpqnmtQ