If what you're looking for realism/verisimilitude in climbing, here's some info:
The purpose of a rope is, of course, to allow one climber to save another if they slip. How you do that depends on the kind of climbing:
If you're on steep ice and snow, you can (maybe?) save your partner by throwing yourself flat and digging axe and crampons into the ice. The most legendary real life episode of this occurred on K2 in 1953, when Peter Schoening saved his 5 teammates:
The Miracle Belay - Gripped Magazine.
In glacier travel the danger isn't slipping and falling off the mountain, but falling into a crevasse covered with snow. In this case it is desirable to put multiple people on the rope so that if one person falls in there is a lot of mass to catch their fall.
If you're actually climbing on near-vertical rock it's basically impossible to catch somebody else with your own strength, especially if they are above you and fall past you. Thus usually one person moves at a time, with the other finding a stance where they can brace themselves against rock if the other one falls.
When the lead climber is climbing above the follower, this takes two forms:
1. The belay is useless. If the lead climber falls they both die. End of story. Thus the old adage "the leader must never fall".
2. If that seems undesirable, the lead climber periodically attaches the rope to the rock (or to a convenient tree), so that the rope can run freely but securely. That way if the leader falls they fall onto this attachment point, and the force of the fall tries to pull the belayer upward, instead of just yanking them off the cliff. (When it's the follower's turn to climb they remove whatever hardware the leader used as they encounter it.)
When the follower is climbing, the leader finds a good stance (or uses hardware to anchor themselves), wraps the rope around their waist for friction (or, in more modern climbing, through a "belay device") and pulls the rope in while the follower follows. In modern climbing you would leave the rope loose so that the follower is really doing their own climbing, but a 19th century guide who is just braced behind a rock, with a static rope (no stretch), belaying around their waist, with the other end is just tied in a loop around the follower's waist, would keep full tension on the rope so that if the client slips there wouldn't be a jolt.
The bit about dynamic vs. static ropes cannot be overemphasized: modern ropes have a lot of stretch so that the force of a fall is distributed. Even a 3 foot fall on a static rope generates HUGE forces (
try imagine jumping off a table and landing with your knees locked out instead of absorbing the impact), and would break spines (especially with a loop around your waist instead of a proper harness), yank out hardware, and certainly pull unanchored partners off cliffs.
