The RS-232 standard allows a secondary channel on a 25-pin connector. Are there any examples where this secondary channel is actually used, in computers resp. devices connected via the serial port? Googling for it mainly turns up "some modems, for administrative purposes, on a slower connection", but I couldn't find specifics, or examples for computers providing it.
You may not be seeing specific platform examples because the use of the secondary channel (like all Standard serial comms) is essentially platform agnostic. It would be found on systems where comms with the remote end, usually a modem-type device, needed to have the baud rate reset or settings adjusted because of parity errors detected at either end (among others).
So, you'd find this used in places where they had a pool of modems, or a critical modem connection to another network. It would also be used on specialty equipment related to things like telephony.
Typically, the modem-type (DCE) equipment would implement this in firmware or hardware via a UART of some sort, and the control end (DTE) could be anything that understood serials comms.
The specs for these are rather obscure and just don't show up on casual web searches.
I thought HP used this for their proprietary serial networking protocol, but I can't find any confirmation of this. It might have just been plain RS-422/485. (Though the secondary line could have been used there, too. I just can't find evidence that it was for any regular HP equipment from the late 80s.)
In addition to things the other answers have mentioned, in the early days of data communication the main channel was sometimes half duplex because the electronics weren't up to more, but there was a secondary channel at a much slower data rate and this line in the RS232 cable was used to control it. BTW, the kind of numbers I'm talking about are a high speed channel at 600 bps half duplex and a secondary channel with rates as low as 1 bps, in that case primarily used to send the one bit message "stop sending, I urgently need to tell you something".
The only information I found so far is about Telebit modems where the secondary channel was used to query modem status while the primary channel was busy with data.
This link reports an email from Telebit staff on configuration guides and mentions several supported machines - although there is no mention of secondary channel it's likely that some of those machines could have had it provided.