Modern Unixes generally support rather elaborate configuration of what swap space is available. FreeBSD supports multiple swap devices and can enable and disable them at runtime (cf swapon(8)), including paging things back in in order to let you disabling a swap device that's in use. Linux can go even further, allowing you to swap to files as well as devices (which takes a bunch of work inside the kernel). It will probably not surprise you to hear that early Unixes were not so sophisticated and featureful, and in fact were rather simple and brute force about things.

(It seems that under the right conditions, FreeBSD will also swap to files, cf the handbook section on creating a swap file.)

In V7, there was a single swap device and that device was hard-coded into the kernel at kernel compilation time, as swapdev in sys/conf/c.c (see sys/conf/mkconf.c). V7 similarly hard-coded the root filesystem device. It doesn't look like V7 had anything to control turning swap on and off; it was on all the time.

In the BSD line, 4.2 BSD had swapon(2) to (selectively) enable swapping, but had no way of turning swapping off on a device once you'd turned it on. It did now support swapping on multiple devices, but the (potential) swap devices were hard coded when you built the kernel, somewhat like V7 (cf eg GENERIC/swaphkvmunix.c and the various configuration files in sys/conf). As in V7, the root filesystem was also hard-coded. This relatively fixed set of swapping options continued through at least 4.3 Tahoe (based on reading manual pages).

Interestingly, swapping to a file goes a long way back in Linux; it's supported in 0.96c (from 1992), according to tuhs.org's copy of mm/swap.c. However, Linux 0.96c only supported a single swap area (whether it was a file or a device), and it doesn't look like you could turn swapping off once you turned it on.

I'm not sure how swap configuration worked in System V, especially before System V Release 4. It turns out that archive.org has System V source code available, and in SVR4 the kernel source code suggests that you can add and delete multiple swap devices and swap files, without any need to configure them into the kernel in advance. This may have been what inspired Linux to support swapping to a file so early on in its life, since System V Release 4 dates from the late 1980s.

(Writing all of this down has gotten me to realize just how long ago all of it was. Unix has had pretty capable swap support for more than 30 years now, if you start from System V Release 4 or Linux.)