Don't expect highly of me so you won't get disappointment.  The 7960 is too new for parts and accessories in circulation with third party sellers.  You can chat with Sales or request a Sales callback https://www.dell.com/en-uk/lp/contact-us

Inquiring the compatibility for this thunderbolt 4 AIC with Manufacturer Part RGF9P | Dell Part 540-BDLC | Order Code 540-Bdlc.  Also verifying if the header cable is included with this CRU kit (it usually does). 

Many thanks for that.  I already have the card, it's the header cable that's proving very difficult to acquire!  There seem to be variants of the cables depending on the platform being used; for instance, I bought a RTWF2 which isn't quite right for the 7960, and I also see there's a 3FMMG which also doesn't look quite right in terms of connectors.  Puzzling.

The header cable RTWF2 can be used together with Dell thunderbolt 4 AIC 7R4VG.  Also is compatible with your 7960.

The problem (as I see it, I may be wrong) is that the RTWF2 has a 14-pin sideband connector, this goes in the AIC, all good so far.  At the other end are a 10-pin USB2 header, and a 10-pin TBT header, which seems to indicate that it's incompatible with the 7960, which has a 14-pin TBT motherboard socket.  Do I just ignore the TBT aspect of this cable?

Found a seller with cable information showing that RTWF2 is compatible with 5860 and 7960 but is not compatible with other systems.  The cable 3FMMG, on the other hand, is compatible with 3650, 3660, but is not with 5860 or 7960.  Because other systems have 10-pin TBT connector, while the 7960 has 14-pin TBT connector. 

https://us.amazon.com/Thunderbolt-Networking-07R4VG-Replacement-Precision/dp/B0CCJQ7M3L

You can test your RTWF2 without the TBT connector if you choose.  Although it's required.

Another note, the TB AIC needs to be on a PCH slot.  Therefore, try slot 2 or slot 3.

Thanks for all of this, I do appreciate it.

Looking at cable 3FMMG, I see a 14-pin sideband connector for the AIC, and 2 connectors from that, a 14-pin (labelled CAC/PIV) and a 10-pin (labelled TBT4).  Not sure what CAC/PIV means in this context, but googling infers some sort of Smart Card interface?

A bit more digging has unearthed another cable - a 2RTV3 (ASSY,CBL,GPIO+USB2,TBT4).  Do you have any images of that?  I can't find any.

CAC/PIV is connector #14 on your system board (see below).  There is a 9-pin section for USB connector.

@Chino de Oro​ I'm missing something here, where's the 9-pin section for the USB connector on that diagram you've shown?

Ah, is the CAC/PIV connector a dual-purpose one?