LOL, this is not a matter of age. Modems connect to modems - that's their job.
True, but modern modems are dumbed down to a degree where they will ONLY go into originate mode if a dial tone is present; send one or more DTMF digits; then a ringing tone.
They will ONLY go into answer mode if the +/- 40 V (min) ringing signal is detected.
The two modems will then perform the V.24bis (or whatever standard) negotiation sequence. This involves sending several test tones and known coded sequences; they will deduce channel conditions (noise profile, near- and far echo, and delay) and adjust the filters and coding schemes accordingly.
Modern hard- and softmodems tend to not let you do this by hand. Noone implements the AT codes that you could force them to do it, or if someone did, good luck finding documentation. I may be wrong, but I have never seen a newish modem tell you how to do this. Things may be different for "professional" (non-consumer) modems. Certainly ones that are in PBX's.
A "telephone line simulator" would certainly do the trick. In fact, I remember seeing DIY instructions for building a "home PBX" in some issue of Elektor in the 90's. That would solve the problem, since it presents the modem with exactly the environment they are expecting to see.
I have a "dumb" line simulator, battery + a few passive components. I wonder if I could make it into a proper "manual" PBX simulator by adding a relay and a ac ringing injector...