For anyone who might still be interested, it seems that the USB-C cable that is used is critical. I was about to declare my purchase of a CAC1333 a failed experiment when I noticed a remark, in a YouTube video that referred to a similar adaptor (https://www.youtube.com/watch?v=w5txt3IEFBY), that the presenter only found one particular cable that worked—he didn’t know why the one he was using worked and others he tried didn’t.
I have accepted that I may not ever get two Apple 27″ Thunderbolt displays to work on my M1 Mac mini, but I also have an LG UltraFine 4K Thunderbolt display (which works fine if connected through either of the mini’s Thunderbolt ports). When I connected the LG display through the CAC1333 to the HDMI port, using the cable that came with the display, nothing appeared to be happening. I connected to the mini via Screen Sharing from another Mac and noticed that the display connection appeared to be in a reset loop—the display was recognised, but almost immediately disconnected, then it was again recognised, then disconnected, and the cycle continued for as long as I wanted to keep watching. That observation didn’t really help me, but I offer it in case it suggests something to someone who’s a bit more in the know about these things that I am.
If I connected the LG display, to either the mini’s Thunderbolt or HDMI port, the latter through the CAC1333 adaptor, using an Apple USB-C to USB-C cable, I saw no activity at all.
After watching the aforementioned video I found another USB-C to USB-C cable, one that had been supplied with a Samsung external SSD. When I used it to connect the LG display to the CAC1333, everything worked as I’d originally hoped it would!
I have no idea what the difference between these cables is. The LG cable has the Thunderbolt symbol on each end, but the others, including the Samsung one that ‘works’, don’t. I can mount the Samsung SSD using either the Apple USB-C to USB-C cable or the Samsung one (I didn’t try with the LG cable), but the Samsung cable is the only one that I could get to successfully connect the LG display through the CAC1333 adaptor to the HDMI port on my M1 mini.
Go figure… although this is not the first time I have been confounded by USB-C cables that look the same but clearly behave differently. USB-C cables are not all created equal…