hello,
some fresh news.
I received my new PBD yesterday and it took 2 min to plug it in my RX: the boot's light came on, then all the rest OK.
So in my case, I am now pretty sure the problem is a component failure in he PBD printed board (temperature sensibility?).
I spent about one hour to replace all element (PBD, plastics, etc...), it is very easy to remove and reinstall.
for information, I bought the PBD at Partsouq, dubai.
461.95USD and 140 USD add for custom
Lexus france told me 1 500 USD only for the part, and 1 800 USD total replacement incl.
In my case it worked and no need to spend further money, 600 USD is quite enough.
if you have some question, don't hesitate.